Geometry Unit 4 Practice Quiz

Name: _________________________
Date: __________________________

Unit 4 Practice Quiz: Triangles

1. Which of the following sets of side lengths can form a triangle?

  1. 3, 4, 8
  2. 6, 8, 14
  3. 7, 8, 10
  4. 5, 5, 10

2. In \(\triangle XYZ\), \(m\angle X = 40^\circ\), \(m\angle Y = 60^\circ\), and \(m\angle Z = 80^\circ\). Which is the shortest side of the triangle?

  1. \(\overline{XY}\)
  2. \(\overline{YZ}\)
  3. \(\overline{XZ}\)
  4. All sides are equal.

3. The measures of the angles in a triangle are \(x\), \(2x\), and \(3x\). What is the measure of the largest angle?

  1. 30°
  2. 60°
  3. 90°
  4. 180°

4. An exterior angle of a triangle measures 100°. If one of the remote interior angles is 60°, what is the measure of the other remote interior angle?

  1. 160°
  2. 80°
  3. 40°
  4. 60°

5. Which postulate proves the two triangles below are congruent?

Description: Two triangles each have a side of length 5, a side of length 7, and the angle between these two sides is 50°.

  1. SSS
  2. SAS
  3. ASA
  4. They are not congruent.

6. Given \(\triangle CAT \cong \triangle DOG\). If \(CA = 10\) and \(DO = 2x - 2\), what is the value of x?

  1. 4
  2. 5
  3. 6
  4. 12

7. You are given that \(\angle A \cong \angle X\) and \(\angle B \cong \angle Y\). What additional information is needed to prove \(\triangle ABC \cong \triangle XYZ\) by ASA?

  1. \(\angle C \cong \angle Z\)
  2. \(\overline{AB} \cong \overline{XY}\)
  3. \(\overline{BC} \cong \overline{YZ}\)
  4. \(\overline{AC} \cong \overline{XZ}\)

8. Given \(\triangle PQR \cong \triangle STU\). If \(m\angle P = (4x + 10)^\circ\) and \(m\angle S = 50^\circ\), find x.

  1. 10
  2. 15
  3. 40
  4. 60

9. Two sides of a triangle are 8 cm and 12 cm. Can the third side be 3 cm long?

  1. Yes, because 8 + 12 > 3.
  2. Yes, because 12 - 8 > 3.
  3. No, because 3 + 8 is not greater than 12.
  4. No, because 3 + 12 > 8.

10. On a coordinate plane, you find that \(\overline{AB} \cong \overline{DE}\), \(\overline{BC} \cong \overline{EF}\), and \(\overline{AC} \cong \overline{DF}\). What can you conclude?

  1. \(\triangle ABC \cong \triangle DEF\) by SSS.
  2. \(\triangle ABC \cong \triangle DEF\) by SAS.
  3. \(\triangle ABC \cong \triangle DEF\) by ASA.
  4. The triangles are not congruent.