GRE Math : Plane Geometry

Example Questions

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle

An acute Isosceles triangle has two sides with length  and one side length . The length of side   inches. If the length of  , what is the perimeter of the triangle?

inches

inches

inches

inches

inches

Explanation:

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 #2 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle

An acute Isosceles triangle has two sides with length  and one side length . The length of side   inches. If the length of , what is the perimeter of the triangle?

feet

feet

inches

inches

inches

inches

Explanation:

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 #1 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle

An acute Isosceles triangle has two sides with length  and one side length . The length of side   ft. If the length of   , what is the perimeter of the triangle?

foot

foot

foot

inches

inches

inches

Explanation:

To solve this problem apply the formula: .

However, first calculate the length of the missing side by:

, Note that

Since, it takes  inches to make one foot, the perimeter is equal to  inches.

Example Question #4 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle

An acute Isosceles triangle has two sides with length  and one side length . The length of side   inches. The length of side  . Find the perimeter of the triangle.

inches

inches

inches

inches

inches

inches

Explanation:

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 #11 : Triangles

The obtuse Isosceles triangle shown above has two sides with length  and one side length . The length of side   inches. Side length . Find the perimeter of the triangle.

inches

inches

inches

inches

inches

inches

Explanation:

To find the perimeter of this triangle, apply the perimeter formula:

Since, , and  then  must have a value of:

This triangle has two side lengths of  inches, and one side length of  inches.

Thus, the solution is:

Example Question #12 : Isosceles Triangles

A triangle has two sides with length  and one side length . The length of side   yard. If the length of   the length of side , what is the perimeter of the triangle?

yard

yard

yard

yard

yard

yard

Explanation:

The first step to solving this problem is that we must find the length of length  Since,  is 4 the length of side , use the following steps:

Now, apply the formula:

Example Question #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

An isosceles triangle has an angle of 110°.  Which of the following angles could also be in the triangle?

35

90

110

20

55

35

Explanation:

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 #2 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

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?

96
42
84
12
20
Explanation:

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 #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Triangle ABC is isosceles

x and y are positive integers

A

---

x

B

---

y

The two quantities are equal

Quantity B is greater

Quantity A is greater

The relationship cannot be determined

Quantity B is greater

Explanation:

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 #4 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

An isosceles triangle has one obtuse angle that is . What is the value of one of the other angles?