Aim: How to prove triangles are congruent using a 3 rd shortcut: ASA.

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# Aim: How to prove triangles are congruent using a 3 rd shortcut: ASA. - PowerPoint PPT Presentation

Aim: How to prove triangles are congruent using a 3 rd shortcut: ASA. Do Now:. Given: T is the midpoint of PQ, PQ bisects RS, and RQ  SP. Explain how RTQ  STP. Do Now. You are given: T is the midpoint of PQ, PQ bisects RS, and RQ  SP. Explain how RTQ  STP.

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Aim: How to prove triangles are congruent using a 3rd shortcut: ASA.

Do Now:

Given:

T is the midpoint of PQ, PQ bisects RS, and RQ  SP. Explain how RTQ  STP.

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

(S  S)

PT  TQ – a midpoint of a segment cuts the segment into two congruent parts

(S  S)

RT  TS – a bisector divides a segment into 2 congruent parts

(S  S)

RTQ  STPbecause of SSS  SSS

A‘

B’

C’

ABC  A’B’C’

Sketch 14 – Shortcut #3

A

B

C

Copied 2 angles and included side:

BC  B’C’, B  B’, C  C’

Measurements showed:

Shortcut for proving congruence in triangles:

ASA  ASA

Angle-Side-Angle

III.ASA = ASA

Two 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

A’

B

C

B’

C’

If A =  A\', AB = A\'B\',  B =  B\', then DABC = DA\'B\'C\'

IfASA  ASA,

then the triangles are congruent

Model Problems

Is the given information sufficient to prove congruent triangles?

YES

YES

NO

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.

DCA  CAB

DFA  BFC

DB  DB

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

C  D – lines form right angles and all right angles are  & equal 90o

(A  A)

CE  ED – bisector cuts segment into 2  parts

(S  S)

CEA  BED – intersecting straight lines form vertical angles which are opposite and 

(A  A)

ACE  BDE because ofASA  ASA

Model Problem

1  2, D is midpoint of EC, 3  4.

Explain how AED  BCD using ASA

1  2 – Given: we’re told so

(A  A)

ED  DC – a midpoint of a segment cuts the segment into two congruent parts

(S  S)

(A  A)

3  4 – Given: we’re told so

AED  BCD because ofASA  ASA

Model Problem

DA is a straight line, E  B, ED  AB, FD  DE, CA  AB

Explain how DEF  ABC using ASA

E  B – Given: we’re told so

(A  A)

ED  AB – Given: we’re told so

(S  S)

EDF  BAC -  lines form right angles and all right angles are  & equal 90o

(A  A)

DEF  ABC because ofASA  ASA