Prove that segment AC bisects segment BD, and that segment BD bisects segment AC using the ASA theorem. I am going to prove that segment AC bisects segment BD, and that segment BD bisects segment AC using the Angle-Side-Angle Triangle Congruence Theorem. D, D2 B1 BD is a transversal of parallel lines AD and CB, so angles ADX and CBX are alternate interior angles, and therefore congruent. By the same reasoning, angles BCX and DAX are congruent. A2 Because ABCD is a parallelogram, I know that segments AD and CB are congruent (opposite sides of a parallelogram are congruent), and lines AD and CB are parallel.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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SectionP.CT: Test
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Place them in order
Prove that segment AC bisects segment BD, and that segment BD bisects segment AC using the ASA theorem.
I am going to prove that segment AC bisects
segment BD, and that segment BD bisects segment
AC using the Angle-Side-Angle Triangle
Congruence Theorem.
D,
B2
D2
B1
BD is a transversal of parallel lines AD and CB, so
- angles ADX and CBX are alternate interior angles,
and therefore congruent. By the same reasoning,
angles BCX and DAX are congruent.
Because ABCD is a parallelogram, I know that
segments AD and CB are congruent (opposite
sides of a parallelogram are congruent), and lines
AD and CB are parallel.
Transcribed Image Text:Prove that segment AC bisects segment BD, and that segment BD bisects segment AC using the ASA theorem. I am going to prove that segment AC bisects segment BD, and that segment BD bisects segment AC using the Angle-Side-Angle Triangle Congruence Theorem. D, B2 D2 B1 BD is a transversal of parallel lines AD and CB, so - angles ADX and CBX are alternate interior angles, and therefore congruent. By the same reasoning, angles BCX and DAX are congruent. Because ABCD is a parallelogram, I know that segments AD and CB are congruent (opposite sides of a parallelogram are congruent), and lines AD and CB are parallel.
Because corresponding parts of congruent triangles
are congruent, segment BX is congruent to
segment DX, so AC bisects BD. By the same
reasoning, segment AX is congruent to segment
CX, so BD bisects AC.
Therefore, triangles AXD and CXB are congruent
by the Angle-Side-Angle Triangle Congruence
Theorem.
Transcribed Image Text:Because corresponding parts of congruent triangles are congruent, segment BX is congruent to segment DX, so AC bisects BD. By the same reasoning, segment AX is congruent to segment CX, so BD bisects AC. Therefore, triangles AXD and CXB are congruent by the Angle-Side-Angle Triangle Congruence Theorem.
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