When a transversal crosses parallel lines, Statement Reason angles are c AB CD and AD | BC Pick angle pair type v Given 22 스 4 When a transversal crosses parallel lines, allel lines, all Pick angle pair type v angles are congruent. Pick angle pair type 3. 21 23 When a transversal crosses parallel lines, alternate interior angles are congruent. corresponding 4 Pick statement v Pick reason v alternate interior 4,3) 5. AABC CDA Angle-side-angle congruence (2,4,3) ent triangles 6. ZB ZD Corresponding parts of congruent triangles are congruent (5). alternate exterior sarne side interior 4 Pick statement ♥ Pick reson v V Pick statement v Pick reason AB=CD Given AC=CA They are corresponding sides between congruent triangles. AD=CB They are lengths of the same segment. Complete the proof that the opposite angles of parallelogram ABCD are congruent. A 1 3 4 C This will prove that ZB ZD.We can use a similar proof for the other pair of opposite angles by using the diagonal BD instead of AC.

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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When a transversal crosses parallel lines,
Statement
Reason
angles are c
AB CD and
AD | BC
Pick angle pair type v
Given
22 스 4
When a transversal crosses parallel lines,
allel lines, all
Pick angle pair type v
angles are congruent.
Pick angle pair type
3.
21 23
When a transversal crosses parallel lines, alternate interior angles are
congruent.
corresponding
4
Pick statement v
Pick reason v
alternate interior
4,3)
5.
AABC CDA
Angle-side-angle congruence (2,4,3)
ent triangles
6.
ZB ZD
Corresponding parts of congruent triangles are congruent (5).
alternate exterior
sarne side interior
4
Pick statement ♥
Pick reson v
V Pick statement
v Pick reason
AB=CD
Given
AC=CA
They are corresponding sides between congruent triangles.
AD=CB
They are lengths of the same segment.
Transcribed Image Text:When a transversal crosses parallel lines, Statement Reason angles are c AB CD and AD | BC Pick angle pair type v Given 22 스 4 When a transversal crosses parallel lines, allel lines, all Pick angle pair type v angles are congruent. Pick angle pair type 3. 21 23 When a transversal crosses parallel lines, alternate interior angles are congruent. corresponding 4 Pick statement v Pick reason v alternate interior 4,3) 5. AABC CDA Angle-side-angle congruence (2,4,3) ent triangles 6. ZB ZD Corresponding parts of congruent triangles are congruent (5). alternate exterior sarne side interior 4 Pick statement ♥ Pick reson v V Pick statement v Pick reason AB=CD Given AC=CA They are corresponding sides between congruent triangles. AD=CB They are lengths of the same segment.
Complete the proof that the opposite angles of parallelogram ABCD are congruent.
A
1
3
4
C
This will prove that ZB ZD.We can use a similar proof for the other pair of opposite angles by using
the diagonal BD instead of AC.
Transcribed Image Text:Complete the proof that the opposite angles of parallelogram ABCD are congruent. A 1 3 4 C This will prove that ZB ZD.We can use a similar proof for the other pair of opposite angles by using the diagonal BD instead of AC.
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