4.5 Using Congruent Triangles

Objectives: - Use congruent triangles to plan and write proofs

Planning a proof

Draw a diagramMark what you knowFigure out what you can prove

Planning & Writing a Proof

Given: AB || DC and BC || DAProve: AB =~ CD

B C

AD

Planning & Writing a Proof

Mark what you know

B C

AD

Planning & Writing a Proof

Deduce what you can:2 pairs of alternate interior angles are congruent

BD is congruent to BD

B C

AD

Planning & Writing a Proof

What does this give?ASA

B C

AD

Another example

1

Given: Angle 1 =~ Angle 2 Angle 3 =~ Angle 4Prove: ∆BCE = ∆DCE

2 34

C

D

E A

B

Mark what you know

1

Given: Angle 1 =~ Angle 2 Angle 3 =~ Angle 4Prove: ∆BCE = ∆DCE

2 34

C

D

E A

B

Figure out what you know

1

What do you know about AC?If you have AC congruent and the 2

angles, what does that give you for triangles ABC and ADC?

If the triangles are congruent, what do you know about BC and DC?

2 34

C

D

E A

B

Figure out what you know

1

If the triangles are congruent, what do you know about BC and DC?

What do you know about CE?If you have BC =~ DC and CE =~ CE and

Angle 1 =~ Angle 2, what does that give you?

2 34

C

D

E A

B

Restate your Given

1

1. Angle 1 =~ Angle 2 Given2. Angle 3 =~ Angle 4 Given

2 34

C

D

E A

B

Write the proof

1

1. Angle 1 =~ Angle 2 Given2. Angle 3 =~ Angle 4 Given3. AC =~ AC Reflexive Property of Congruence4. ∆ABC =~ ∆ADC ASA5. CE =~ CE Reflexive Property of Congruence6. ∆BCE =~ ∆DCE SAS

2 3

4C

D

E A

B

Do p. 232 1-3, 28

Classwork: p. 232 4-18 evensHomework - 2 worksheets