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

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 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 #3A

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

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

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