Question

C R Given: AC = AR and Z1 = Z2 3 A Prove: Z3 = 24 L S

Answer 1

Lines CS and LR form vertical angles.

Vertical angles are pairs of opposite angles made by intersecting lines. If two angles are vertical then they are congruent (Have the same measure)

Then:

$\angle5\cong\angle6$

In a triangle the sum of it's internal angles is always 180º.

$\begin{gathered} \angle1+\angle3+\angle5=180º \\ \angle2+\angle4+\angle6=180º \end{gathered}$

Then, as:

$\begin{gathered} \angle1\cong\angle2 \\ \angle5\cong\angle6 \\ \\ \end{gathered}$

The angles 3 and 4 are congruents too:

$\angle3\cong\angle4$