Question

Proving trapezoid theorems Geometry

Answer 1

Answer:

ΔABD ≅ ΔACD by SAS, therefore;

$\overline {BD} \cong \overline {CA}$ by CPCTC

Step-by-step explanation:

The two column proof is presented as follows;

Statement ${}$                   Reason

ABCD is a trapezoid ${}$  Given

$\overline {BA} \cong \overline {CD}$  ${}$                   Given

$\overline {BC} \parallel \overline {AD}$   ${}$                   Definition of a trapezoid

ABCD is an isosceles trapezoid  ${}$    Left and right leg are equal

∠BAD ≅ ∠CDA  ${}$          Base angle of an isosceles trapezoid are congruent

$\overline {AD} \cong \overline {AD}$   ${}$                  Reflexive property

ΔABD ≅ ΔACD   ${}$         By SAS rule of congruency

$\overline {BD} \cong \overline {CA}$   ${}$                  CPCTC

CPCTC; Congruent Parts of Congruent Triangles are Congruent

SAS; Side Angle Side rule of congruency

Answer 2

Answer:

Step-by-step explanation:

just did it