Practice with Congruent Triangles

1. List the five criteria for triangle congruence and draw a picture that demonstrates each.

2. Given two triangles, do you always need at least three pieces of information about each triangle in order to be able to state that the triangles are congruent?

For each pair of triangles, tell whether the given information is enough to show that the triangles are congruent. If the triangles are congruent, state the criterion that you used to determine the congruence and write a congruency statement.

Note that the images are not necessarily drawn to scale.

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For 9-11, state whether the given information about a hidden triangle would be enough for you to construct a triangle that must be congruent to the hidden triangle. Explain your answer.

9. \(\triangle A B C\) with \(m \angle A=72^{\circ}, A B=6 cm , B C=8 cm\).

10. \(\triangle A B C\) with \(m \angle A=90^{\circ}, A B=4 cm , B C=5 cm\).

11. \(\triangle A B C\) with \(m \angle A=72^{\circ}, A B=6 cm , A C=8 cm\).

Source: CK-12, https://flexbooks.ck12.org/cbook/ck-12-interactive-geometry-for-ccss/section/3.5/primary/lesson/applications-of-congruent-triangles-geo-ccss/

 This work is licensed under CK-12 Curriculum Materials License.

1. The five criteria are AAS, \(ASA , \, SAS , \, SSS\), and for right triangles \(HL\). Pictures vary.

2. Yes. Note that while \(HL\) has only two letters, you also need to know that the triangles are right triangles.

3. \(\triangle EIF \cong \triangle HFI\) by \(AAS\).

4. Not enough information.

5. \(\triangle ABC \cong \triangle ADC\) by \(SSS\).

6. \(\triangle ABC \cong \triangle ADC\) by \(SAS\).

7. \(\triangle ACB \cong \triangle ACD\) by \(ASA\).

8. Not enough information.

9. Not enough information.

10. Yes, by \(HL\).

11. Yes, by \(SAS\).