How to find if two acute / obtuse triangles are similar - Math
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The ratio of the side lengths of a triangle is 7:10:11. In a similar triangle, the middle side is 9 inches long. What is the length of the longest side of the second triangle?
The ratio of the side lengths of a triangle is 7:10:11. In a similar triangle, the middle side is 9 inches long. What is the length of the longest side of the second triangle?
Side lengths of similar triangles can be expressed in proportions. Establish a proportion comparing the middle and long sides of your triangles.
10/11 = 9/x
Cross multiply and solve for x.
10x = 99
x = 9.9
Side lengths of similar triangles can be expressed in proportions. Establish a proportion comparing the middle and long sides of your triangles.
10/11 = 9/x
Cross multiply and solve for x.
10x = 99
x = 9.9
Compare your answer with the correct one above
and 
are similar triangles. The perimeter of Triangle A is 45” and the length of two of its sides are 15” and 10”. If the perimeter of Triangle B is 135” and what are lengths of two of its sides?
The perimeter is equal to the sum of the three sides. In similar triangles, each side is in proportion to its correlating side. The perimeters are also in equal proportion.
Perimeter A = 45” and perimeter B = 135”
The proportion of Perimeter A to Perimeter B is 
.
This applies to the sides of the triangle. Therefore to get the any side of Triangle B, just multiply the correlating side by 3.
15” x 3 = 45”
10” x 3 = 30“
The perimeter is equal to the sum of the three sides. In similar triangles, each side is in proportion to its correlating side. The perimeters are also in equal proportion.
Perimeter A = 45” and perimeter B = 135”
The proportion of Perimeter A to Perimeter B is
This applies to the sides of the triangle. Therefore to get the any side of Triangle B, just multiply the correlating side by 3.
15” x 3 = 45”
10” x 3 = 30“
Compare your answer with the correct one above
Two triangles are similar to each other. The bigger one has side lengths of 12, 3, and 14.
The smaller triangle's shortest side is 1 unit in length. What is the length of the smaller triangle's longest side?
Two triangles are similar to each other. The bigger one has side lengths of 12, 3, and 14.
The smaller triangle's shortest side is 1 unit in length. What is the length of the smaller triangle's longest side?
Because the triangles are similar, a ratio can be set up between the triangles' longest sides and shortest sides as such: 14/3 = x/1. Solving for x, we obtain that the shortest side of the triangle is 14/3 units long.
Because the triangles are similar, a ratio can be set up between the triangles' longest sides and shortest sides as such: 14/3 = x/1. Solving for x, we obtain that the shortest side of the triangle is 14/3 units long.
Compare your answer with the correct one above
A triangle with two equal angles is called a(n) __________.
A triangle with two equal angles is called a(n) __________.
An isoceles triangle is a triangle that has at least two congruent sides (and therefore, at least two congruent angles as well).
An isoceles triangle is a triangle that has at least two congruent sides (and therefore, at least two congruent angles as well).
Compare your answer with the correct one above
Are the triangles similar? If so, solve for 
. (Not drawn to scale).
Are the triangles similar? If so, solve for
The triangles are similar because of the side-angle-side postulate.
Side: 
Angle: 
Side: 
The third side must also have a 2:3 ratio.
Cross-multiply, and solve for 
.
The triangles are similar because of the side-angle-side postulate.
Side:
Angle:
Side:
The third side must also have a 2:3 ratio.
Cross-multiply, and solve for
Compare your answer with the correct one above
Are the triangles similar? If so, solve for 
. (Not drawn to scale).
Are the triangles similar? If so, solve for
The triangles are not similar, as proven by the side-side-side postulate.
The third side does not follow the same ratio of the other two, thus the triangles are not similar.
The triangles are not similar, as proven by the side-side-side postulate.
The third side does not follow the same ratio of the other two, thus the triangles are not similar.
Compare your answer with the correct one above
The following triangles are similar. Which postulate proves their similarity?
The following triangles are similar. Which postulate proves their similarity?
Angle-Angle Postulate: if two angles of one triangle are equal to two corresponding angles of another triangle, the triangles must be similar.
In this example, the triangles share one angle, which must be equal. Additionally, the triangles contain segments that are parallel to each other. When two parallel lines are crossed by another line, the corresponding angles must be equal. Each angle in one triangle is congruent with its corresponding angle in the other triangle, indicating that they are similar.
Angle-Angle Postulate: if two angles of one triangle are equal to two corresponding angles of another triangle, the triangles must be similar.
In this example, the triangles share one angle, which must be equal. Additionally, the triangles contain segments that are parallel to each other. When two parallel lines are crossed by another line, the corresponding angles must be equal. Each angle in one triangle is congruent with its corresponding angle in the other triangle, indicating that they are similar.
Compare your answer with the correct one above
The following triangles are similar. Which postulate proves their similarity?
The following triangles are similar. Which postulate proves their similarity?
The Side-Angle-Side Postulate considers two corresponding sides and the included angle. The included angles must be congruent, and the ratios of the two corresponding sides must be equal. If both criteria are satisfied, then the triangles are similar.
In this problem, there is a shared angle, making it equal for the two triangles. Now, consider the ratios of the sides.
![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/91032/gif.latex "\frac{4}{10}\ =\ or\
eq \frac{6}{15}")
Simplify the fractions.
because the ratios are equal, the triangles are similar by the Side-Angle-Side postulate.
The Side-Angle-Side Postulate considers two corresponding sides and the included angle. The included angles must be congruent, and the ratios of the two corresponding sides must be equal. If both criteria are satisfied, then the triangles are similar.
In this problem, there is a shared angle, making it equal for the two triangles. Now, consider the ratios of the sides.
Simplify the fractions.
because the ratios are equal, the triangles are similar by the Side-Angle-Side postulate.
Compare your answer with the correct one above
The ratio of the side lengths of a triangle is 7:10:11. In a similar triangle, the middle side is 9 inches long. What is the length of the longest side of the second triangle?
The ratio of the side lengths of a triangle is 7:10:11. In a similar triangle, the middle side is 9 inches long. What is the length of the longest side of the second triangle?
Side lengths of similar triangles can be expressed in proportions. Establish a proportion comparing the middle and long sides of your triangles.
10/11 = 9/x
Cross multiply and solve for x.
10x = 99
x = 9.9
Side lengths of similar triangles can be expressed in proportions. Establish a proportion comparing the middle and long sides of your triangles.
10/11 = 9/x
Cross multiply and solve for x.
10x = 99
x = 9.9
Compare your answer with the correct one above
and are similar triangles. The perimeter of Triangle A is 45” and the length of two of its sides are 15” and 10”. If the perimeter of Triangle B is 135” and what are lengths of two of its sides?
The perimeter is equal to the sum of the three sides. In similar triangles, each side is in proportion to its correlating side. The perimeters are also in equal proportion.
Perimeter A = 45” and perimeter B = 135”
The proportion of Perimeter A to Perimeter B is .
This applies to the sides of the triangle. Therefore to get the any side of Triangle B, just multiply the correlating side by 3.
15” x 3 = 45”
10” x 3 = 30“
The perimeter is equal to the sum of the three sides. In similar triangles, each side is in proportion to its correlating side. The perimeters are also in equal proportion.
Perimeter A = 45” and perimeter B = 135”
The proportion of Perimeter A to Perimeter B is
This applies to the sides of the triangle. Therefore to get the any side of Triangle B, just multiply the correlating side by 3.
15” x 3 = 45”
10” x 3 = 30“
Compare your answer with the correct one above
Two triangles are similar to each other. The bigger one has side lengths of 12, 3, and 14.
The smaller triangle's shortest side is 1 unit in length. What is the length of the smaller triangle's longest side?
Two triangles are similar to each other. The bigger one has side lengths of 12, 3, and 14.
The smaller triangle's shortest side is 1 unit in length. What is the length of the smaller triangle's longest side?
Because the triangles are similar, a ratio can be set up between the triangles' longest sides and shortest sides as such: 14/3 = x/1. Solving for x, we obtain that the shortest side of the triangle is 14/3 units long.
Because the triangles are similar, a ratio can be set up between the triangles' longest sides and shortest sides as such: 14/3 = x/1. Solving for x, we obtain that the shortest side of the triangle is 14/3 units long.
Compare your answer with the correct one above
A triangle with two equal angles is called a(n) __________.
A triangle with two equal angles is called a(n) __________.
An isoceles triangle is a triangle that has at least two congruent sides (and therefore, at least two congruent angles as well).
An isoceles triangle is a triangle that has at least two congruent sides (and therefore, at least two congruent angles as well).
Compare your answer with the correct one above
Are the triangles similar? If so, solve for . (Not drawn to scale).
Are the triangles similar? If so, solve for
The triangles are similar because of the side-angle-side postulate.
Side:
Angle:
Side:
The third side must also have a 2:3 ratio.
Cross-multiply, and solve for .
The triangles are similar because of the side-angle-side postulate.
Side:
Angle:
Side:
The third side must also have a 2:3 ratio.
Cross-multiply, and solve for
Compare your answer with the correct one above
Are the triangles similar? If so, solve for . (Not drawn to scale).
Are the triangles similar? If so, solve for
The triangles are not similar, as proven by the side-side-side postulate.
The third side does not follow the same ratio of the other two, thus the triangles are not similar.
The triangles are not similar, as proven by the side-side-side postulate.
The third side does not follow the same ratio of the other two, thus the triangles are not similar.
Compare your answer with the correct one above
The following triangles are similar. Which postulate proves their similarity?
The following triangles are similar. Which postulate proves their similarity?
Angle-Angle Postulate: if two angles of one triangle are equal to two corresponding angles of another triangle, the triangles must be similar.
In this example, the triangles share one angle, which must be equal. Additionally, the triangles contain segments that are parallel to each other. When two parallel lines are crossed by another line, the corresponding angles must be equal. Each angle in one triangle is congruent with its corresponding angle in the other triangle, indicating that they are similar.
Angle-Angle Postulate: if two angles of one triangle are equal to two corresponding angles of another triangle, the triangles must be similar.
In this example, the triangles share one angle, which must be equal. Additionally, the triangles contain segments that are parallel to each other. When two parallel lines are crossed by another line, the corresponding angles must be equal. Each angle in one triangle is congruent with its corresponding angle in the other triangle, indicating that they are similar.
Compare your answer with the correct one above
The following triangles are similar. Which postulate proves their similarity?
The following triangles are similar. Which postulate proves their similarity?
The Side-Angle-Side Postulate considers two corresponding sides and the included angle. The included angles must be congruent, and the ratios of the two corresponding sides must be equal. If both criteria are satisfied, then the triangles are similar.
In this problem, there is a shared angle, making it equal for the two triangles. Now, consider the ratios of the sides.
Simplify the fractions.
because the ratios are equal, the triangles are similar by the Side-Angle-Side postulate.
The Side-Angle-Side Postulate considers two corresponding sides and the included angle. The included angles must be congruent, and the ratios of the two corresponding sides must be equal. If both criteria are satisfied, then the triangles are similar.
In this problem, there is a shared angle, making it equal for the two triangles. Now, consider the ratios of the sides.
Simplify the fractions.
because the ratios are equal, the triangles are similar by the Side-Angle-Side postulate.
Compare your answer with the correct one above
The ratio of the side lengths of a triangle is 7:10:11. In a similar triangle, the middle side is 9 inches long. What is the length of the longest side of the second triangle?
The ratio of the side lengths of a triangle is 7:10:11. In a similar triangle, the middle side is 9 inches long. What is the length of the longest side of the second triangle?
Side lengths of similar triangles can be expressed in proportions. Establish a proportion comparing the middle and long sides of your triangles.
10/11 = 9/x
Cross multiply and solve for x.
10x = 99
x = 9.9
Side lengths of similar triangles can be expressed in proportions. Establish a proportion comparing the middle and long sides of your triangles.
10/11 = 9/x
Cross multiply and solve for x.
10x = 99
x = 9.9
Compare your answer with the correct one above
and are similar triangles. The perimeter of Triangle A is 45” and the length of two of its sides are 15” and 10”. If the perimeter of Triangle B is 135” and what are lengths of two of its sides?
The perimeter is equal to the sum of the three sides. In similar triangles, each side is in proportion to its correlating side. The perimeters are also in equal proportion.
Perimeter A = 45” and perimeter B = 135”
The proportion of Perimeter A to Perimeter B is .
This applies to the sides of the triangle. Therefore to get the any side of Triangle B, just multiply the correlating side by 3.
15” x 3 = 45”
10” x 3 = 30“
The perimeter is equal to the sum of the three sides. In similar triangles, each side is in proportion to its correlating side. The perimeters are also in equal proportion.
Perimeter A = 45” and perimeter B = 135”
The proportion of Perimeter A to Perimeter B is
This applies to the sides of the triangle. Therefore to get the any side of Triangle B, just multiply the correlating side by 3.
15” x 3 = 45”
10” x 3 = 30“
Compare your answer with the correct one above
Two triangles are similar to each other. The bigger one has side lengths of 12, 3, and 14.
The smaller triangle's shortest side is 1 unit in length. What is the length of the smaller triangle's longest side?
Two triangles are similar to each other. The bigger one has side lengths of 12, 3, and 14.
The smaller triangle's shortest side is 1 unit in length. What is the length of the smaller triangle's longest side?
Because the triangles are similar, a ratio can be set up between the triangles' longest sides and shortest sides as such: 14/3 = x/1. Solving for x, we obtain that the shortest side of the triangle is 14/3 units long.
Because the triangles are similar, a ratio can be set up between the triangles' longest sides and shortest sides as such: 14/3 = x/1. Solving for x, we obtain that the shortest side of the triangle is 14/3 units long.
Compare your answer with the correct one above
A triangle with two equal angles is called a(n) __________.
A triangle with two equal angles is called a(n) __________.
An isoceles triangle is a triangle that has at least two congruent sides (and therefore, at least two congruent angles as well).
An isoceles triangle is a triangle that has at least two congruent sides (and therefore, at least two congruent angles as well).
Compare your answer with the correct one above