High School Math : High School Math
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Example Questions
Example Question #353 : Plane Geometry
The following triangles are similar. Which postulate proves their similarity?
Side-Angle-Side Postulate
Angle-Angle Postulate
Side-Side-Side Postulate
Side-Side-Angle Postulate
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.
Example Question #354 : Plane Geometry
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?
9
7.7
12.1
10
9.9
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
Example Question #355 : Plane Geometry
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.
Example Question #1 : Isosceles Triangles
A triangle with two equal angles is called a(n) __________.
right triangle
disjoint triangle
equilateral triangle
Pythagoras triangle
isosceles triangle
isosceles triangle
An isoceles triangle is a triangle that has at least two congruent sides (and therefore, at least two congruent angles as well).
Example Question #143 : Sat Mathematics
Find the height of a triangle if the area of the triangle = 18 and the base = 4.
9
1
4
6
9
The area of a triangle = (1/2)bh where b is base and h is height. 18 = (1/2)4h which gives us 36 = 4h so h =9.
Example Question #891 : High School Math
Simplify the exponential expression below.
The power rule of exponents states that when an exponential term is raised to another power, we multiply the exponents to simplify.
Example Question #2 : Polynomials
What is the value of 
The power rule says that an exponent to the power of another exponent gets multiplied. We can think of 
Example Question #3 : Polynomials
Simplify 
When raising a polynomial to a power you multiply the polynomial inside the parentheses by the power outside of the parentheses.
If you think about it 
So we multiply 
The answer is 
Example Question #4 : Polynomials
Simplify the expression.
The power rule of exponents states than an exponential term raised to another exponent can be simplified by multiplying the exponents together.
Example Question #5 : Polynomials
What is 
When raising a polynomial to a power you multiply the polynomial inside the parentheses by the power outside of the parentheses.
So we multiply 
The answer is 
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