1. 4.5
ANSWER Yes; HL Thm.
4.5 Prove Triangles Congruent by ASA and AAS
Bell Thinger
Tell whether the pair of triangles is congruent or not
and why.
ANSWER yes; SSS
1. 2.

2. 4.5

3. 4.5

4. 4.5Example 1
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.
a.

5. 4.5
Can the triangles be proven congruent with the
information given in the diagram? If so, state the
postulate or theorem you would use.
SOLUTION
b. There is not enough information to prove the
triangles are congruent, because no sides are
known to be congruent.
Example 1

6. 4.5
Can the triangles be proven congruent with the
information given in the diagram? If so, state the
postulate or theorem you would use.
SOLUTION
c. Two pairs of angles and their included sides are
congruent. The triangles are congruent by the ASA
Congruence Postulate.
Example 1

7. 4.5

8. 4.5Example 2
Prove the Angle-Angle-Side Congruence Theorem.
GIVEN: A ≅ D, C ≅ F,
BC ≅ EF
PROVE: ABC DEF

9. 4.5Guided Practice
1. In the diagram at the right, what
postulate or theorem can you use to
prove that RST ≅ VUT? Explain.
ANSWER AAS; ∠RTS and ∠VTU are also congruent
because they are also vertical angles.

10. 4.5Example 3
In the diagram, CE BD and CAB ≅ CAD.
Write a flow proof to show ABE ≅ ADE.
GIVEN: CE BD, CAB ≅ CAD
PROVE: ABE ≅ ADE

11. 4.5Example 4
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.

12. 4.5Example 4
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.
The correct answer is B.ANSWER

13. 4.5

14. 4.5
Tell whether each pair of triangle are congruent by
SAS, ASA, SSS, AAS or HL. If it is not possible to prove
the triangle congruent, write not necessarily
congruent.
ANSWER ASA
1.
Exit Slip

15. 4.5
Tell whether each pair of triangle are congruent by
SAS, ASA, SSS, AAS or HL. If it is not possible to prove
the triangle congruent, write not necessarily
congruent.
ANSWER not necessarily congruent
2.
Exit Slip

16. 4.5
Homework
Pg 262-265
#18, 19, 20, 24, 26