Question

#3: given: $overline{ac}congoverline{ar}$ and $angle1congangle2$ prove: $angle3congangle4$ proof: 1. $overline{ac}congoverline{ar}$ 2. 3. $angle calcongangle ras$ 4. $\triangle lcacong\triangle sra$ 5. $angle3congangle4$

Explanation:

Step1: Given side - equality

$\overline{AC}\cong\overline{AR}$ (Given)

Step2: Given angle - equality

$\angle1\cong\angle2$ (Given, not shown in the steps list but part of given info for the proof)

Step3: Common - angle

$\angle CAL=\angle RAS$ (They are the same angle, reflexive property of angles)

Step4: Prove triangle congruence

$\triangle LCA\cong\triangle SRA$ by the Angle - Side - Angle (ASA) congruence criterion since we have $\overline{AC}\cong\overline{AR}$, $\angle CAL\cong\angle RAS$ and $\angle1\cong\angle2$

Step5: Corresponding parts of congruent triangles

Since $\triangle LCA\cong\triangle SRA$, then $\angle3\cong\angle4$ (Corresponding parts of congruent triangles are congruent, CPCTC)

Answer:

$\angle3\cong\angle4$