Question

Proving trapezoid theorems Geometry

Answer 1

Explanation:

just did it

Answer 2

ΔABD ≅ ΔACD by SAS, therefore;

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

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