Question

Use a paragraph, flow chart, or two-column proof to prove the angle congruency. Given: ∠ CXY ≅ ∠ BXY

Answer 1

Answer:

See explanation

Step-by-step explanation:

Consider triangles CAX and BAX. In these triangles,

• $\overline{AC}\cong \overline{AB}$ - given
• $\angle CAX\cong \angle BAX$ - given
• $\overline{AX}\cong \overline{AX}$ - reflexive property

By SAS postulate, $\triangle CAX\cong \triangle BAX$

Congruent triangles have conruent corresponding parts. So,

$\overline{CX}\cong \overline{BX}$

Consider triangles CXY and BXY. In these triangles,

• $\overline{CX}\cong \overline{BX}$ - proven
• $\angle CXY\cong \angle BXY$ - given
• $\overline{XY}\cong \overline{XY}$ - reflexive property

By SAS postulate, $\triangle CXY\cong \triangle BXY$

Congruent triangles have conruent corresponding parts. So,

$\angle XCY\cong \angle XBY$