Free Printable G.6 Congruent Triangles

1.

Define: Base Angles Theorem

a)

If two sides of a triangle are congruent, then the angles opposite them are congruent.

b)

If three sides of a triangle are congruent, then the angles opposite them are congruent.

c)

If one side of a triangle are congruent, then the angles opposite them are congruent.

d)

If no sides of a triangle are congruent, then the angles opposite them are congruent.

2.

Define: Side-Side-Side (SSS) Congruence Postulate

a)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

b)

If two sides of a triangle are congruent, then the angles opposite them are congruent.

c)

If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

d)

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

3.

Define: Corollary to the Base Angles Theorem

a)

If two sides of a triangle are congruent, then the angles opposite them are congruent.

b)

The sum of the measures of the interior angles of a triangle is 180 degrees.

c)

If a triangle is equiangular, then it is equilateral.

d)

If a triangle is equilateral, then it is equiangular.

4.

Define: Angle-Angle-Side (AAS) Congruence Theorem

a)

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangles, then the three triangles are congruent.

b)

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangles, then the two triangles are congruent.

c)

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangles, then the single triangle is congruent.

d)

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangles, then all four triangles are congruent.

5.

Define: Corollary to the Converse of the Base Angles Theorem

a)

If a triangle is equilateral, then it is equiangular.

b)

If a triangle is equiangular, then it is equilateral.

c)

The sum of the measures of the interior angles of a triangle is 180 degrees.

d)

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

6.

Define: Side-Angle-Side (SAS) Congruence Postulate

a)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are similar.

b)

If three sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

c)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

d)

If two sides and the included angle of one triangle are congruent to three sides and the included angle of a second triangle, then the two triangles are congruent.

7.

Define: Angle-Side-Angle (ASA) Congruence Postulate

a)

If two angles and the included side of one triangle are congruent to two angles and the non-included side of a second triangle, then the two triangles are congruent.

b)

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are similar.

c)

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

d)

If two angles and the included side of onetriangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

8.

Define: Congruent Triangles to Prove Corresponding Parts Congruent (CPCTC)

a)

CTCPC can be used to show corresponding parts of congruent triangles congruent.

b)

CPCTC can be used to show corresponding parts of congruent triangles congruent.

c)

CPCTC can be used to show corresponding sides of congruent triangles congruent.

d)

CPCTC can be used to show corresponding parts of congruent triangles congruent.

9.

Define: Third Angles Theorem

a)

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

b)

If three angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

c)

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also similar.

d)

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

10.

Define: Triangle Sum Theorem

a)

The sum of the measures of the interior angles of a triangle is 360 degrees.

b)

The sum of the measures of the interior angles of a triangle is 180 degrees.

c)

The sum of the measures of the exterior angles of a triangle is 180 degrees.

d)

The product of the measures of the interior angles of a triangle is 180 degrees.

11.

Define: Hypotenuse-Leg (HL) Congruence Theorem

a)

If the hypotenuse and a leg of a scalene triangle are congruent to the hypotenuse and a leg of a second triangle, then the two triangles are congruent.

b)

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the two triangles are similar.

c)

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a third triangle, then the two triangles are congruent.

d)

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the two triangles are congruent.

12.

Define: Exterior Angles Theorem

a)

The measure of an exterior angle of a triangle is equal to the difference of the measures of the two nonadjacent interior angles.

b)

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two adjacent interior angles.

c)

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

d)

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent supplementary angles.

13.

Given:
<S and <T are right angles.
Line RV and Line VU are congruent
Prove: ΔRSV is congruent to ΔTVU

a)

1) Given
2)<RVS is congruent to <UVT
3)<R is congruent to <U
4) ASA

b)

1) Given
2) <RVS is not congruent to <UVT
3) SAS

c)

1) Given
2)<RVS is congruent to <UVT
3)<R is congruent to <U
4) AAS

d)

1) Given
2)<RVS is congruent to <UVT
3)<R is congruent to <U
4) SSA

14.

Which of the following can not be used to prove that two triangles are congruent?

a)

Angle-Angle-Side (AAS)

b)

Side-Angle-Side (SAS)

c)

Angle-Angle-Angle (AAA)

d)

Side-Side-Side (SSS)

15.

Is Angle-Angle-Angle (AAA), a valid rule for proving triangles congruent?

a)

No

b)

Sometimes

c)

Yes

d)

N/A

16.

In Δs GHI and JKL, line HI is congruent to line KL, line GI is congruent to line JL, and <I is congruent to <L. ΔHGI is congruent to Δ...?

a)

KLJ

b)

KJL

c)

JKL

d)

LJK

17.

Is Side-Side-Angle (SSA), a valid rule for proving triangles congruent?

a)

N/A

b)

Yes

c)

No

d)

Sometimes

18.

Use the given coordinates to determine if ΔABC is congruent to ΔPQR.
A(-2,1), B(2,6), C(6,2)
P(-1,-2), Q(3,3) R(7,-1)

a)

No

b)

Yes

19.

In an isosceles triangles, the base angles are equivalent. One of the sides is equal to 3x+15 while the other is 4x+12. What is the value of x?

a)

4

b)

3

c)

33

d)

10

20.

In a equilateral triangle, all lengths are equal to 8. The two base angles are equal to 6x and 8x-22. What is the value of x?

a)

10

b)

12

c)

13

d)

11

21.

In rhombus ABCD, line BC is congruent to line AB, and <B is congruent to <D. BD is one of the rhombus' diagonals. Decide if the triangles are congruent, if yes, what postulate/theorem could be used, if no, why?

a)

No, because not all the angles are given.

b)

Yes, SSA.

c)

Yes, SAS.

d)

Yes, ASA.

22.

Given: line WX is congruent to line XY, line XZ bisects <WXY.
Prove: line XZ bisects line WY

a)

1. line XZ bisects <WXY - Given
2. <WXZ is congruent to <YXZ - Definition of angle bisector
3. line WX is congruent to line XY - Given
4. <W is congruent to <Y - Definition of an isosceles triangle
5. ΔWXZ is congruent to ΔYXZ - ASA
6. line WZ is congruent to line YZ - CPCTC
7. line XZ bisects line WY - Definition of segment bisector

b)

1. line XZ bisects <WXY - Given
2. <WXZ is congruent to <YXZ - Definition of angle bisector
3. line WX is congruent to line XY - Given
4. <W is congruent to <Y - Definition of an isosceles triangle
5. ΔWXZ is congruent to ΔYXZ - ASA
6. line WZ is congruent to line YZ - CPCTC
7. line XZ bisects <WY - Definition of segment bisector

c)

1. line XZ bisects <WXY - Given
2. <WXZ is congruent to <YXZ - Definition of angle bisector
3. line WX is congruent to line XY - Given
4. <W is congruent to <Y - Definition of an isosceles triangle
5. ΔWXZ is congruent to ΔYXZ - ASA
6. line WZ is congruent to line YZ - CPCTC
7. line XZ bisects line WY - Definition of angle bisector

d)

1. line XZ bisects <WXY - Given
2. <WXZ is congruent to <YXZ - Definition of angle bisector
3. line WX is congruent to line XY - Given
4. <W is congruent to <Y - Definition of an isosceles triangle
5. ΔWXZ is congruent to ΔYXZ - ASA
6. line WZ is congruent to line YZ - CPCTC
7. line XZ bisects line WY - Segment Bisector Postu

23.

In rectangle PQMN, given: line MN is congruent to line PQ, and line MQ is congruent to line NP
Prove: ΔMNQ is congruent to ΔPQN

a)

1. line MN is congruent to PQ; line MQ is congruent to line NP - Given
2. line QN is congruent to NQ - Reflexive Property of Equality
3. ΔMNQ is congruent to PQN - Side-Side-Side (SSS)

b)

1. line MN is congruent to PQ; line MQ is congruent to line NP - Given
2. line QN is congruent to NQ - Reflexive Property of Congruence
3. ΔMNQ is congruent to PQN - Angle-Angle-Side (AAS)

c)

1. line MN is congruent to PQ; line MQ is congruent to line NP - Given
2. line QN is congruent to NQ - Reflexive Property of Congruence
3. ΔMNQ is congruent to PQN - Side-Side-Side (SSS)

d)

1. line MN is congruent to PQ; line MQ is congruent to line NP - Given
2. line QN is congruent to NQ - Reflexive Property of Congruence
3. ΔMNQ is congruent to PQN - Side-Side-Angle (SSA)

24.

In ΔAZC, line ZB runs down to line AC. <A and <C are congruent, and line AZ and line ZC are congruent. Decide if the triangles are congruent, if yes, what postulate/theorem could be used, if no, why?

a)

Yes, AAA.

b)

No, because line ZB may not be an < bisector.

c)

Yes, SAS.

d)

Yes, SSS.

25.

In ΔABC, there are lines BN, LC, MA, and centered Q. QC = 6. Find CL.

a)

CL = 8

b)

CL = 12

c)

CL = 6

d)

CL = 9

G.6 Congruent Triangles

Total questions: 25

Worksheet time: 23mins

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