82.7k views
4 votes
C R Given: AC = AR and Z1 = Z2 3 A Prove: Z3 = 24 L S

C R Given: AC = AR and Z1 = Z2 3 A Prove: Z3 = 24 L S-example-1
User Cina
by
3.5k points

1 Answer

0 votes

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

C R Given: AC = AR and Z1 = Z2 3 A Prove: Z3 = 24 L S-example-1
User Mikhail Sidorov
by
3.3k points