1. 5.3 Congruent Triangles & Proof
Tools needed for today:
Pencil
protractor

2. Are your triangles the same?
Exploration
Use your straightedge to draw AB 7 cm long.
Now use your protractor to draw <A= 70o.
Next, draw AC 5 cm long.
Use your straightedge to connect B to C.
Compare your triangle ABC to your neighbor’s triangle ABC.
Are your triangles the same?

3. Were all of the triangles congruent?
WHY?
Side-Angle-Side (SAS) Congruence Theorem:
If two sides and the included angle of one triangle are
congruent to two sides and the included angle of a
second triangle, then the two triangles are congruent.

4. Example 1 Given: Prove: Statements Reasons 1. 2. 3. Given 4.
Alternate Interior Angles Theorem
Reflexive Property of Congruence
∆𝐴𝐵𝐶≅∆𝐶𝐷𝐴
SAS Congruence Theorem

5. Example 2 Given: Prove: C is the midpoint of Statements Reasons and1. 2. 3. 4.
C is the midpoint of
Given
and
Definition of midpoint
Vertical Angles are congruent
SAS Congruence Theorem

6. Now it’s your turn! Book p 249 #2 – 18 even 16 & 18 are proofs…
be sure to make & label a table for your proof.