1. Tell whether the pair of triangles is congruent or not and why.
ANSWER
Yes; HL Thm.

2. EXAMPLE 1
Identify congruent triangles
Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.
SOLUTION
The vertical angles are congruent, so two pairs of angles and a pair of non-included sides are congruent. The triangles are congruent by the AAS Congruence Theorem.

3. EXAMPLE 1
Identify congruent triangles
There is not enough information to prove the triangles are congruent, because no sides are known to be congruent.
Two pairs of angles and their included sides are congruent. The triangles are congruent by the ASA Congruence Postulate.

4. EXAMPLE 2
Prove the AAS Congruence Theorem
Prove the Angle-Angle-Side Congruence Theorem.
GIVEN
BC EF
A D,
C F,
PROVE
ABC DEF

5. GUIDED PRACTICE
for Examples 1 and 2
In the diagram at the right, what postulate or theorem can you use to prove that
RST VUT
? Explain.
AAS; are congruent because they are vertical angles.
RTS and VTU
ANSWER

6. GUIDED PRACTICE
for Examples 1 and 2
Rewrite the proof of the Triangle Sum Theorem as a flow proof.
GIVEN
ABC
PROVE 3
= 180° 1 m 2 +

7. GUIDED PRACTICE
for Examples 1 and 2

8. EXAMPLE 3
Write a flow proof
In the diagram, CE BD and CAB CAD.
Write a flow proof to show
ABE ADE
GIVEN
CE BD,
CAB CAD
PROVE
ABE ADE

9. EXAMPLE 4
Standardized Test Practice

10. EXAMPLE 4
Standardized Test Practice
The locations of tower A, tower B, and the fire form a triangle. The dispatcher knows the distance from tower A to tower B and the measures of A and B. So, the measures of two angles and an included side of the triangle are known.
By the ASA Congruence Postulate, all triangles with these measures are congruent. So, the triangle formed is unique and the fire location is given by the third vertex. Two lookouts are needed to locate the fire.

11. EXAMPLE 4
Standardized Test Practice
ANSWER
The correct answer is B.

12. GUIDED PRACTICE
for Examples 3 and 4
In Example 3, suppose ABE ADE is also given. What theorem or postulate besides ASA can you use to prove that
ABE ADE?
ANSWER
AAS Congruence Theorem.

13. GUIDED PRACTICE
for Examples 3 and 4
WHAT IF? In Example 4, suppose a fire occurs directly between tower B and tower C. Could towers B and C be used to locate the fire? Explain
ANSWER
No; no triangle is formed by the location of the fire and towers, so the fire could be anywhere between towers B and C.

14. Daily Homework Quiz
Tell whether each pair of triangles is congruent by SAS, ASA, SSS, AAS or HL. If it is not possible to prove the triangles congruent, write not necessarily congruent. 1.
ANSWER
ASA

15. Daily Homework Quiz
Tell whether each pair of triangles is congruent by SAS, ASA, SSS, AAS or HL. If it is not possible to prove the triangles congruent, write not necessarily congruent. 2.
ANSWER
not necessarily congruent

16. Daily Homework Quiz 3.
Write a flow proof.
Given : BD bisects ABC, A C
Prove : ABD CBD

17. Daily Homework Quiz
ANSWER