4.5

ANSWER Yes; HL Thm.

4.5 Prove Triangles Congruent by ASA and AASBell Thinger

Tell whether the pair of triangles is congruent or not and why.

ANSWER yes; SSS

1. 2.

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4.5

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.

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

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

4.5

4.5Example 2

Prove the Angle-Angle-Side Congruence Theorem.

GIVEN: A ≅ D, C ≅ F,

BC ≅ EF

PROVE: ABC DEF

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 congruentbecause they are also vertical angles.

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

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.

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

4.5

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

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

4.5

HomeworkPg 262-265 #18, 19, 20, 24, 26