DSQ: Calculating whether right triangles are congruent

Practice Questions

GMAT Quantitative Reasoning › DSQ: Calculating whether right triangles are congruent

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Altitude

Note: Figure NOT drawn to scale.

Refer to the above diagram.

True or false: $\Delta ABX \cong \Delta ACX$

Statement 1: $\overline{AX}$ is the perpendicular bisector of $\overline{BC}$ .

Statement 2: $\overline{AX}$ is the bisector of $\angle CAB$ .

2

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with right angles $\angle B, \angle E$

True or false: $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Statement 1: $\left (DE \right ) ^{2} +(EF) ^{2} = \left ( AC\right )^{2}$

Statement 2: $\left ( AC \right )^{2} - \left ( AB\right )^{2} > \left ( EF\right )^{2}$

3

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with right angles $\angle B, \angle E$

True or false: $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Statement 1: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ have the same area.

Statement 2:

4

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with right angles $\angle B, \angle E$

True or false: $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Statement 1:

Statement 2:

5

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with right angles $\angle B, \angle E$

True or false: $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Statement 1:

Statement 2:

6

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with right angles $\angle B, \angle E$

True or false: $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Statement 1: $\left (AB \right ) ^{2} +(BC) ^{2} = \left ( DF\right )^{2}$

Statement 2: $\left ( DF\right )^{2} - \left ( DE\right )^{2} = \left ( BC\right )^{2}$

7

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with right angles $\angle B, \angle E$

True or false: $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Statement 1: $\angle A$ and $\angle F$ are complementary angles.

Statement 2:

8

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with right angles $\angle B, \angle E$

True or false: $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Statement 1: A single circle can be constructed that passes through and .

Statement 2:

9

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with right angles $\angle B, \angle E$

True or false: $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Statement 1: and .

Statement 2:

10

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with right angles $\angle B, \angle E$

True or false: $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Statement 1:

Statement 2:

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