Given: R is the midpoint of line SU ; angles SVU is isosceles with base line SU Prove: angles RSV is congruent to angles RUV

Question

Given: R is the midpoint of line SU ; angles SVU is isosceles with base line SU

 

Prove: angles RSV is congruent to angles RUV

Answer 1

draw line segment SU

draw isosceles triangle SVU

put in point R as the midpoint of line segment SU

draw line segment VR

proof:

you have 2 triangles, triangle SRV and triangle URV

SR≅RU   R is the midpoint of segment SU (given)

SV≅VU   triangle SVU is isosceles  (given) and an isosceles triangle has 2 congruent sides and segment SU is the base meaning SV and VU are the congruent sides

VR≅VR   reflexive property

triangle SRV≅triangle URV   SSS (side, side, side theorem)

<RSV≅<RUV   corresponding angles of congruent triangles are congruent  (RSV and RUV are corresponding angles because they are the angles opposite the congruent sides in the isosceles triangle)