GRE Math : Plane Geometry
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Example Questions
Example Question #4 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle
An acute Isosceles triangle has two sides with length 
In order to solve this problem, first find the length of the missing sides. Then apply the formula:
The missing side equals:
Then plug each side length into the perimeter formula:
Example Question #3 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle
An acute Isosceles triangle has two sides with length 
In order to solve this problem, first find the length of the missing sides. Then apply the formula:
The missing side equals:
Then, apply the perimeter formula by plugging in the side values:
Example Question #4 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle
An acute Isosceles triangle has two sides with length 
To solve this problem apply the formula: 
However, first calculate the length of the missing side by:
Since, it takes 
Example Question #3 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle
An acute Isosceles triangle has two sides with length 
To find the perimeter of this triangle, apply the formula:
Note: Since this is an acute Isosceles triangle, the length of the base must be smaller than the length of both of the equivalent sides.
Example Question #61 : Geometry
The obtuse Isosceles triangle shown above has two sides with length 
To find the perimeter of this triangle, apply the perimeter formula:
Since, 
This triangle has two side lengths of 
Thus, the solution is:
Example Question #11 : Isosceles Triangles
A triangle has two sides with length 
The first step to solving this problem is that we must find the length of length 
Now, apply the formula:
Example Question #11 : Triangles
An isosceles triangle has an angle of 110°. Which of the following angles could also be in the triangle?
110
35
20
90
55
35
An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.
Example Question #12 : Triangles
An isosceles triangle ABC is laid flat on its base. Given that <B, located in the lower left corner, is 84 degrees, what is the measurement of the top angle, <A?
Since the triangle is isosceles, and <A is located at the top of the triangle that is on its base, <B and <C are equivalent. Since <B is 84 degrees, <C is also. There are 180 degrees in a triangle so 180 - 84 - 84 = 12 degrees.
Example Question #13 : Triangles
Triangle ABC is isosceles
x and y are positive integers
A
---
x
B
---
y
Quantity A is greater
The two quantities are equal
The relationship cannot be determined
Quantity B is greater
Quantity B is greater
Since we are given expressions for the two congruent angles of the isosceles triangle, we can set the expressions equal to see how x relates to y. We get,
x – 3 = y – 7 --> y = x + 4
Logically, y must be the greater number if it takes x an additional 4 units to reach its value (knowing they are both positive integers).
Example Question #14 : Triangles
An isosceles triangle has one obtuse angle that is 
We know that an isosceles triangel has two equal sides and thus two equal angles opposite those equal sides. Because there is one obtuse angle of 112 degrees we automatically know that this angle is the vertex. If you sum any triangle's interior angles, you always get 180 degrees.
180 – 112 = 68 degrees. Thus there are 68 degrees left for the two equal angles. Each angle must therefore measure 34 degrees.
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