Given: a // b & s // t Prove: 4 @ 13 1 9 10 2 a 3 4 11 - - PowerPoint PPT Presentation

Given: a // b & s // t Prove: 4 @ 13

1 3 b a t s 5 7 8 6 4 2 9 10 11 12 13 14 16 15

Congruent Figures -

Figures that have the same size and shape. Hypothesize with your partner…what do you think is true, specifically, about these two congruent triangles.

B A C D E F DABC @ DDEF

• 1. Identify the corresponding parts of congruent

figures. 2.Formally prove triangles are congruent using postulates and theorems. 3.Deduce information about segments and angles after proving that two triangles are congruent. 4.Apply the following vocabulary terms – median, altitude, perpendicular bisector. 5.Refine proof construction skills.

Observations -

B A C D E F

A @ B @ C @

3in 4in 5in 5in 4in 3in 90° 90° 37° 53° 37° 53°

AB @ BC @ AC @ DE EF DF

D E F

DABC @ DDEF

Conclusion

Corresponding Parts of Congruent Triangles are Congruent.

Practice - CPCTC

A C T O D G Given: DCAT @ DDOG CA @ C @ CT @ A @ AT @ T @

Two triangles are congruent if and only if their vertices can be matched up so that the corresponding parts (angles and sides) of the triangles are congruent.

G O D DO DG OG

Practice - CPCTC

Given: DPIG @ DCOW PG @ P @ PI @ I @ IG @ G @ CW CO OW C O W

How else could you name the congruent triangles?

DPIG @ DCOW DGIP @ DWOC DIPG @ DOCW DPIG @ DWOC DGIP @ DCOW DGPI @ DWCO DPGI @ DCWO DIGP @ DOWC DIPG @ DWCO

Make sure the letters match up!!

Practice - CPCTC

B N U A T G

DBUG @

AN @ GB A @ G AT @ GU N @ B NT @ BU T @ U

DNTA

Partner Practice

• p. 119 # 1-11

#11 – Write a Proof!

• p. 119 # 1-4

DFIN @ DWEB

1.Name the three pairs of corresponding sides. FI @ IN @ FN @

• 2. Name the three pairs of corresponding angles.

F @ I @ N @

• 3. Is it correct to say DNIF @ DBEW?
• 4. Is it correct to say DINF @ DEWB?

No Yes

B E W

WB EB WE

• Yes. O is the midpoint of

AC and DB because AO = OC and DO = OB.

• p. 119 # 5 - 9

A B O D C

• 5. DABO @
• 6. A @
• 7. AO @
• 8. BO @
• 9. Can you deduce that

O is the midpoint of any segment? DCDO C CO DO

• p. 119 # 10

A B O D C

• 10. Explain how you can deduce that DC // AB.

A @ C If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

• 11. Suppose you know that DB ^ DC. Explain

how you can deduce that DB ^ BA.

• 2. D is a right angle
• 2. Definition of perpendicular lines.
• 4. mD = mB
• 4. CPCTC
• 7. Definition of perpendicular lines.
• 5. mB = 90
• 5. Substitution
• 1. DB ^ DC; DABO @ DCDO
• 1. Given
• 7. DB ^ BA
• 3. mD = 90
• 3. Definition of a Right Angle
• 6. B is a right angle
• 6. Definition of a Right Angle

A B O D C

Something to think about…

B C D E A F G H J K

What do you think might be true about

• ther congruent polygons? Such as two

congruent pentagons.

HW

• p. 120 WE

#1-8, 10, 11, 20, 21, 23 Draw all diagrams.