Aim: Triangle Congruence - ASA Course: Applied Geometry
Do Now:
Aim: How to prove triangles are congruent using a 3rd shortcut: ASA.
Given:T is the midpoint of PQ, PQ bisects RS, and RQ SP. Explain how RTQ STP.
T
P S
R Q
Aim: Triangle Congruence - ASA Course: Applied Geometry
Do Now
You are given:T is the midpoint of PQ, PQ bisects RS, and RQ SP. Explain how RTQ STP.
RQ SP – we’re told so
PT TQ – a midpoint of a segment cuts the segment into two congruent parts
RT TS – a bisector divides a segment into 2 congruent parts
RTQ STP because of SSS SSS
(S S)
(S S)
(S S)
T
P S
R Q
Aim: Triangle Congruence - ASA Course: Applied Geometry
Sketch 14 – Shortcut #3
ASA ASAASA ASA
Copied 2 angles and included side:
BC B’C’, B B’, C C’
Copied 2 angles and included side:
BC B’C’, B B’, C C’
Shortcut for proving congruence in triangles:
Measurements showed:
B
A
C
B’
A‘
C’
ABC A’B’C’ABC A’B’C’
Aim: Triangle Congruence - ASA Course: Applied Geometry
Angle-Side-Angle
III. ASA = ASATwo triangles are congruent if two angles and the included side of one triangle are equal in measure to two angles and the
included side of the other triangle.A
B B’C C’
A’
If A = A', AB = A'B', B = B', then ABC = A'B'C'
If ASA ASA , then the triangles are congruent
Aim: Triangle Congruence - ASA Course: Applied Geometry
Model Problems
Is the given information sufficient to prove congruent triangles?
F
D EA B
C
DA B
C
E
C
D
B
A
YES
YES
NO
Aim: Triangle Congruence - ASA Course: Applied Geometry
Model Problems
Name the pair of corresponding sides that would have to be proved congruent in order to prove that the triangles are congruent by ASA.
D C
A B
F
D
C
B
A
D C
A B
DCA CAB
DFA BFC
DB DB
Aim: Triangle Congruence - ASA Course: Applied Geometry
Model Problem
CD and AB are straight lines which intersect at E. BA bisects CD. AC CD, BD CD.Explain how ACE BDE using ASA
CE ED – bisector cuts segment into 2 parts
C D – lines form right angles and all right angles are & equal 90o
ACE BDE because of ASA ASA
(S S)
(A A)
E D
B
C
A
CEA BED – intersecting straight lines form vertical angles which are opposite and (A A)
Aim: Triangle Congruence - ASA Course: Applied Geometry
Model Problem
1 2, D is midpoint of EC, 3 4.Explain how AED BCD using ASA
ED DC – a midpoint of a segment cuts the segment into two congruent parts
1 2 – Given: we’re told so
AED BCD because of ASA ASA
(S S)
(A A)
3 4 – Given: we’re told so (A A)
2431
A
DE C
B
Aim: Triangle Congruence - ASA Course: Applied Geometry
Model Problem
DA is a straight line, E B, ED AB, FD DE, CA ABExplain how DEF ABC using ASA
EDF BAC - lines form right angles and all right angles are & equal 90o
DEF ABC because of ASA ASA
(A A)
D
BA
F
E
C
E B – Given: we’re told so (A A)
ED AB – Given: we’re told so (S S)
Aim: Triangle Congruence - ASA Course: Applied Geometry