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Page 1 of 9
Activity 3.1.6 Angle-Angle-Side Congruency
1. Determine the measure of A. m∠𝐴 = ______.
2. Determine the measure of D. m∠𝐷 = ______.
3. Determine the measure of I. m∠𝐼 = ______.
4. Can you make any conclusions? Write your thoughts down about the relationships
between the triangles and the given information.
5. Discuss your ideas with a classmate and try to formalize your ideas into a theorem that
can be communicated with the rest of the class.
6. If _____ angles from one triangle are equal to _____ angles from another triangle, then
their third angles are ______.
Activity 3.1.6
Connecticut Core Geometry Curriculum Version 3.0
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Page 2 of 9
7. Using this new theorem formed in question 6, how can we prove congruence between the
following triangles?
Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹
Given: ∠𝐴 = ∠𝐷, ∠𝐵 = ∠𝐸, 𝐵𝐶 = 𝐸𝐹
{HINT: Use the theorem on the previous page to help you obtain the information necessary for a
previously proven method of congruence}
You have now proved the AAS Congruence Theorem: It two angles and a non-included
_____ of one triangle are congruent to two ______ and the corresponding non-included
______of a second triangle, then the two triangles are congruent.
Activity 3.1.6
Connecticut Core Geometry Curriculum Version 3.0
Name:
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Page 3 of 9
Proving Congruency using SAS, ASA, SSS, and AAS
8. Can the following congruence statement be
proved using the given information and the
diagram? If so, prove the congruence statement.
If not, state why not.
Prove: ∆𝐶𝐵𝐷 ≅ ∆𝐶𝐴𝐸
̅̅̅̅ .
Given: ∠𝐴 = ∠𝐵 and C is the midpoint of segment 𝐴𝐵
Activity 3.1.6
Connecticut Core Geometry Curriculum Version 3.0
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Page 4 of 9
9. Can the following congruence statement be proved using the given information and the
diagram? If so, prove the congruence statement. If not, state why not.
Prove: ∆𝐶𝐵𝐷 ≅ ∆𝐶𝐴𝐸
Given: ∠𝐴 = ∠𝐵 and 𝐵𝐷 = 𝐴𝐸
Activity 3.1.6
Connecticut Core Geometry Curriculum Version 3.0
Name:
Date:
Page 5 of 9
10. Can the following congruence statement be proved using the given information and the
diagram? If so, prove the congruence statement. If not, state why not
Prove: ∆𝐶𝐵𝐷 ≅ ∆𝐶𝐴𝐸
Given: C is the midpoint of segment ̅̅̅̅
𝐴𝐵 and 𝐵𝐷 = 𝐴𝐸
Activity 3.1.6
Connecticut Core Geometry Curriculum Version 3.0
Name:
Date:
Page 6 of 9
11. Can the following congruence statement be proved using the given information and the
diagram? If so, prove the congruence statement. If not, state why not
Prove: ∆𝐴𝐵𝐹 ≅ ∆𝐸𝐻𝐺
Given: m ∠𝐻 = m ∠𝐵 and 𝐹𝐺 = 𝐴𝐸; angles HEG and FAB are right angles.
Activity 3.1.6
Connecticut Core Geometry Curriculum Version 3.0
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Page 7 of 9
12. Can the following congruence statement be proved using the given information and the
diagram? If so, prove the congruence statement. If not, state why not.
Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐴𝐷𝐶
Given: Segment ̅̅̅̅
𝐴𝐶 bisects ∠𝐵𝐴𝐷 and
̅̅̅̅ bisects ∠𝐵𝐶𝐷
Segment 𝐴𝐶
Activity 3.1.6
Connecticut Core Geometry Curriculum Version 3.0
Name:
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Page 8 of 9
13. Can the following congruence statement be proved using the given information and the
diagram? If so, prove the congruence statement. If not, state why not.
Prove: ∠𝐵 ≅ ∠𝐶
Given: 𝐴𝐶 = 𝐴𝐵 and 𝐸𝐴 = 𝐷𝐴
Activity 3.1.6
Connecticut Core Geometry Curriculum Version 3.0
Name:
Date:
Page 9 of 9
14. Can the following congruence statement be proved using the given information and the
diagram? If so, prove the congruence statement. If not, state why not.
Given: ∆𝐴𝐵𝐷 is an equilateral triangle and E is the midpoint of
segment ̅̅̅̅
𝐴𝐷
Prove: ̅̅̅̅
𝐸𝐵 bisects ∠𝐷𝐵𝐴.
15. In question 14 above prove that ̅̅̅̅
𝐸𝐵 ⊥ ̅̅̅̅
𝐴𝐷 .
Activity 3.1.6
Connecticut Core Geometry Curriculum Version 3.0