Question

name:
lesson 8:more triangle congruence proofs
cool down: write a flow chart or two - column proof
given: ( angle a cong angle o )
( overline{ac} cong overline{oc} )
prove: ( angle t cong angle w )

Explanation:

Step1: Vertical angles

$\angle ACT\cong\angle OCW$ (Vertical angles are congruent)

Step2: ASA congruence

In $\triangle ACT$ and $\triangle OCW$:

• $\angle A\cong\angle O$ (Given)
• $AC\cong OC$ (Given)
• $\angle ACT\cong\angle OCW$ (From Step1)

So, $\triangle ACT\cong\triangle OCW$ (ASA - Angle - Side - Angle congruence criterion)

Step3: Corresponding parts of congruent triangles

Since $\triangle ACT\cong\triangle OCW$, then $\angle T\cong\angle W$ (Corresponding parts of congruent triangles are congruent)

Answer:

$\angle T\cong\angle W$ is proved as above.