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Congruent Triangles Worksheet

Congruent Triangles Worksheet
• Page 1
1.
Which of the following cannot be used to prove that two triangles are congruent?
 a. AAS congruence postulate b. SAS congruence postulate c. SSS congruence postulate d. AAA congruence postulate

Solution:

AAA congruence postulate cannot be used to prove that two triangles are congruent.

2.
Which pair of triangles shows congruency by the SAS postulate?

 a. Figure D b. Figure C c. Figure B d. Figure A

Solution:

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
[SAS Postulate.]

The triangles of figure C are congruent by SAS postulate.

3.
ΔABC $\cong$ ΔDEF as shown. Find $x$.

 a. 45o b. 60o c. 75o d. 30o

Solution:

Triangles ABC & DEF are congruent.
[Given.]

mA + mB + mC = 180
[Triangle Angle Sum Theorem.]

mA = 180 - (mB + mC) = 180 - (60 + 45)
[Substitute 60 for mB and 45 for mC.]

mA = 75
[Simplify.]

mD = mA
[ΔABC ΔDEF.]

x = 75o
[Substitute x for mD and 75 for mA .]

4.
Which postulate can be used to prove the triangles congruent?

 a. ASA postulate b. SSS postulate c. SAS postulate d. AAS postulate

Solution:

In the triangles QPR BAC, QRP BCA and PR AC.
[Given.]

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
[ASA postulate.]

So, Δ PQR Δ ABC as per ASA postulate.

5.
What is the length of side BC?

 a. 3 units b. 6 units c. 4 units d. 2 units

Solution:

BC DF.
[ΔDEF ΔBAC.]

Corresponding sides of congruent triangles are congruent.

So, BC = DF = 6
[Substitute 6 for DF.]

6.
Name two pairs of congruent triangles in the figure.

 a. ΔAED, ΔDEC; ΔBEC, ΔBEA b. ΔAED, ΔAEB; ΔBEC, ΔCED c. ΔDEC, ΔBEC; ΔAED, ΔDEC d. ΔDEC, ΔBEA; ΔBEC, ΔDEA

Solution:

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
[SSS postulate.]

ΔDEC ΔBEA and ΔBEC ΔDEA.
[From the figure.]

7.
Which of the following can be used to prove that ΔABC $\cong$ ΔADC ?

 a. ASA postulate b. SAS postulate c. AAS postulate d. SSS postulate

Solution:

BAC DAC
[Given.]

[Given.]

AC AC
[Reflexive property of congruence.]

If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.
[AAS postulate.]

ΔABC ΔADC due to AAS postulate.
[From step 4.]

8.
Which of the following is / are true?
1. A triangle is congruent to itself
2. An isoceles triangle has two congruent correspondances
3. An equilateral triangle has six congruent correspondances
 a. all are true b. 1 and 2 only c. 1 and 3 only d. 1 only

Solution:

A triangle is congruent to itself.

Two angles and two sides are congruent for an isosceles triangle. So, it has two congruent correspondances.

An equilateral triangle has all the sides and all the angles congruent. All the six correspondances of the equilateral triangle are congruent.

So, all the statements are true.

9.
Which of the following can be used to prove Δ PQR $\cong$ ΔABC ?

 a. SSS postulate b. ASA postulate c. SAS postulate d. AAS postulate

Solution:

PQR ABC,
PRQ ACB
and PR AC.
[Given.]

If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.
[AAS theorem.]

So, ΔPQR ΔABC due to AAS postulate.

10.
Which of the following sets of triangles are congruent?

 a. Figure D b. Figure B c. Figure A d. Figure C

Solution:

If three sides of one triangle are congruent to three sides of another, then the two triangles are congruent.
[SSS postulate.]

Triangles in Figure-C are congruent.
[From step1.]