Unit 4 Test Review

Triangle Types

100

Question:

Classify a triangle with three equal sides by its sides and its angles.

Equilateral Equiangular

200

Question:

Classify a triangle with sides 4 cm, 4 cm, and 7 cm by its sides.

Isosceles 

300

A triangle has angles 40°, 60°, and 80°. Classify by angles and by sides.

Scalene and acute.

400

Explain the difference between an isosceles triangle and a scalene triangle.

Isosceles has two equal sides; scalene has no equal sides.

500

A triangle has two congruent angles and all different side lengths. Is this possible and why?
 

 No, congruent angles imply the opposite sides are congruent.

SOLVING FOR X

100

Two sides measure x+3 and 11. They are congruent. Solve for x.

x=8

200

Triangle angles are 3x, 2x+10, and 50°. Find x

x=24

300

Triangle with sides 5, 5, and 2x−1. Find x if it is equilateral.

x=3

400

In triangle PQR, PQ=3x-1 and PR= x+10. If PQ=PR, solve for x.

x= 5.5

500

Triangle DEF: DE = 2x+3, DF= 4x+1. If DE = DF, find x.

x=1

TRIANGLE ANGLES

100

A right triangle has one acute angle of 35°. Find the other acute angle.
 

55°

200

Isosceles triangle with vertex angle 58°. Find each base angle.
 

61°

300

Triangle angles are in ratio 2:3:4. Find all angles.
 

40°, 60°, 80°

400

Angle A = 3x, Angle C = B + 20, Angle B= x. Find all angles.
 

A = 96°, B = 32°, C = 52°

500

Exterior angle = sum of remote interior angles (45° and 70°). Find exterior angle and its linear-pair partner.
 

Exterior = 115°, linear pair = 65°

CONGRUENT OR NOT?

100

100
What congruence postulate uses three pairs of sides?

Side Side Side (SSS)

200

Two right triangles with congruent hypotenuse and a leg.

HL 

300

Two sides and a non-included angle (SSA). Can this prove congruence?
 

 No, SSA is not always valid

400

AB=DE, BC=EF, and <B=<E. What proves them congruent?

Side Angle Side (SAS)

500

If △JKL≅△MNP name three corresponding congruent parts.

JK ≅ MN, KL ≅ NP, JL ≅ MP (angles also acceptable)

Proof Time

100

If AB=CD and CD=EF, then AB=EF. What property?
 

Transitive Property

200

Angles A ≅ D, B ≅ E, and AB = DE. What congruence theorem?
 

AAS

300

OM bisects angle AOB. What angles are congruent?

∠AOM ≅ ∠BOM

400

Given AB = AC, prove ∠B = ∠C. What type of triangle is this?

Isosceles triangle → base angles congruent

500

Given AB = AC and ∠BAD = ∠CAD, prove BD = CD. What is the reason?
 

Triangles congruent by SAS