GMAT Quantitative Reasoning - DSQ: Calculating whether right triangles are similar

1

Given: $\bigtriangleup ABC$ and $\bigtriangleup XYZ$ , where $\angle B$ and $\angle Y$ are right angles.

True or false: $\bigtriangleup ABC \sim \bigtriangleup XYZ$

Statement 1: $m \angle A = 45^{\circ }$

Statement 2: $\bigtriangleup XYZ$ is an isosceles triangle.

2

Triangles and circles

Note: Figure NOT drawn to scale.

Refer to the above figure, which shows two right triangles circumscribed by circles.

True or false: $\bigtriangleup ABC \sim \bigtriangleup XYZ$

Statement 1: The area of the circle that circumscribes $\bigtriangleup ABC$ is four times the that of the circle that circumscribes $\bigtriangleup XYZ$ .

Statement 2: $AB = 2 \cdot DE$

3

Triangles and circles

Note: Figure NOT drawn to scale.

Refer to the above diagram.

True or false: $\bigtriangleup ABC \sim \bigtriangleup DEF$

Statement 1: Arcs $\widehat{AC}$ and $\widehat{DF}$ have the same degree measure.

Statement 2: Arcs $\widehat{ACB}$ and $\widehat{DFE}$ have the same degree measure.

4

Given: $\bigtriangleup ABC$ and $\bigtriangleup XYZ$ , where $\angle B$ and $\angle Y$ are right angles.

True or false: $\bigtriangleup ABC \sim \bigtriangleup XYZ$

Statement 1: Both triangles are scalene.

Statement 2: The triangles have the same perimeter.

5

Given: $\bigtriangleup ABC$ and $\bigtriangleup XYZ$ , where $\angle B$ and $\angle Y$ are right angles.

True or false: $\bigtriangleup ABC \sim \bigtriangleup XYZ$

Statement 1:

Statement 2: $\angle A cong \angle X$

6

You are given two right triangles: $\triangle ABC$ with right angle , and $\triangle XYZ$ with right angle .

True or false: $\triangle ABC \sim \triangle XYZ$

Statement 1: $3 \cdot AB = 4 \cdot XY$

Statement 2: $4 \cdot BC= 3 \cdot YZ$

7

You are given two right triangles: $\triangle ABC$ with right angle , and $\triangle XYZ$ with right angle .

True or false: $\triangle ABC \sim \triangle XYZ$

Statement 1: $\angle A \cong \angle X$

Statement 2: $\angle B \cong \angle Y$

8

You are given two right triangles: $\triangle ABC$ with right angle , and $\triangle XYZ$ with right angle .

True or false: $\triangle ABC \sim \triangle XYZ$

Statement 1: $\angle A$ and $\angle Y$ are complimentary.

Statement 2: $\angle B$ and $\angle X$ are complimentary.

9

Triangle 2

Note: Figure NOT drawn to scale.

Refer to the above figure. True or false: $\bigtriangleup AVB \sim \bigtriangleup CVD$ .

Statement 1: Quadrilateral is a trapezoid.

Statement 2: $\frac{AC}{CV} = \frac{BD}{DV}$

10

Given: Rectangles and with diagonals $\overline{AC}$ and $\overline{EG}$ , respectively.

True or false: $\bigtriangleup ABC \sim \bigtriangleup EFG$

Statement 1: Of the two rectangles, only Rectangle is a rhombus.

Statement 2:

DSQ: Calculating whether right triangles are similar

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