Question

Proving Trapezoid Theorems

Given: ABCD is a trapezoid.
BA
CD
Prove: BD
CA
B
The statement is part of this proof,
O but at least one other statement must
come before it
Clear
Angles Segments Triangles Statements Reasons
given
base angles theorem
Statements
ABCD is an
isosceles trapezoid
reflexive property
def, of isosceles trapezoid
Reasons
reflexive property

Answer 1

Explanation:

To complete the proof, we need to show that BD is congruent to CA. Here's one possible way to complete the proof:

Clear

Angles Segments Triangles Statements Reasons

given

base angles theorem

Statements

ABCD is an

isosceles trapezoid

reflexive property

def, of isosceles trapezoid

BD = AC

def, of isosceles trapezoid

B

Reasons

reflexive property

Since ABCD is an isosceles trapezoid, the legs AB and CD are congruent. By the base angles theorem, angles B and C are congruent. Therefore, triangles ABD and CDA are congruent by the angle-side-angle (ASA) postulate. This means that BD is congruent to AC. Hence, we can write BD = AC. This completes the proof.