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Unit 4 Day by Day

Day Sections and Objectives Homework

Monday

October 26

U4D1

4.2 and 4.9 Packet Pages 1-3

Types of triangles, isosceles and

equilateral triangles

Page 228 (23-31, 35-37)

Page 288 (5-10, 17-20, 22-26)

Wednesday

October 28

½ Day

U4D2

4.3 and 4.4 Packet Pages 4-7

Sum of interior angles of a triangle

Exterior Angel Theorem

Congruent Triangles

Page 236 (19-24, 41-44)

Page 242 (11, 17-19, 23-25, 31-34)

Friday

October 30

U4D3

4.5-4.7 Packet Pages8-15

SSS, SAS, AAS, ASA, HL, CPCTC

Finish Packet Pages 11-15

Tuesday

November 3

U4D4

Quiz 4.2-4.4 and 4.9

Review

Page 247 (5-17

Page 288 (13-16, 42-44)

Wednesday

November 4

U4D5

Review Packet Pages8-15

Friday

November 6

U4D6

Quiz 4.2-4.9

Review

Tuesday

November 10

U4D7

Test Unit 4

None

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Chapter 4 – Congruent Triangles

4.2 and 4.9 – Classifying and Angle Relationships within Triangles.

Isosceles triangles are triangles with two congruent sides.

The two congruent sides are called legs.

The third side is the base.

The two angles at the base are called base angles.

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Match the letter of the figure to the correct vocabulary word in Exercises 1–4.

1. right triangle __________

2. obtuse triangle __________

3. acute triangle __________

4. equiangular triangle __________

Classify each triangle by its angle measures as acute, equiangular, right, or obtuse. (Note: Give two

classifications for Exercise 7.)

5. 6. 7.

For Exercises 8–10, fill in the blanks to complete each definition.

8. An isosceles triangle has ____________________ congruent sides.

9. An ____________________ triangle has three congruent sides.

10. A ____________________ triangle has no congruent sides.

Classify each triangle by its side lengths as equilateral, isosceles, or scalene. (Note: Give two

classifications in Exercise 13.)

11. 12. 13.

Find the side lengths of the triangle.

14. AB ____________________ AC ___________________ BC ______________

15. Given: ABC is isosceles with base AB ; EBDA

Prove: EBCDAC

16. In isosceles ∆PQR, P is the vertex angle. If mQ = 8x – 4 and mR = 5x + 14, find the mP.

17. In isosceles triangle CAT, C is the vertex angle. If A = 8x – 4 and mT = 5x + 14, then what is the

measure of C?

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3. mX __________ 4. BC __________ mA __________

5. PQ __________ 6. mK __________ t __________

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4.3 and 4.4 – Angle Relationships and Congruent Triangles.

The interior is the set of all points inside the figure. The exterior is the set of all points

outside the figure.

An interior angle is formed by two sides of a triangle.

An exterior angle is formed by one side of the triangle and extension of an adjacent side.

Each exterior angle has two remote interior angles. A remote interior angle is an

interior angle that is not adjacent to the exterior angle.

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Congruent Triangles: Two ’s are if their vertices can be matched up so that corresponding angles and sides of the ’s are .

Congruence Statement: RED FOX

List the corresponding ’s: corresponding sides:

R ___ RE ____

E ___ ED ____

D ___ RD ____

Examples:

1. The two ’s shown are .

a) ABO _____ b) A ____

c) AO _____ d) BO = ____

2. The pentagons shown are .

a) B corresponds to ____ b) BLACK _______

c) ______ = mE d) KB = ____ cm

e) If CA LA , name two right ’s in the figures.

3. Given BIG CAT, BI = 14, IG = 18, BG = 21, CT = 2x + 7. Find x.

The following ’s are , complete the congruence statement:

4. YWZ_______

5. MQN _______

6. WTA ________

Parts of a Triangle in terms of their relative positions.

7. Name the opposite side to C.

8. Name the included side between A and B.

9. Name the opposite angle to BC .

D C

O

B A

B

L A

C

K

H

O

R

S

Y X

Z W M N O

P Q W

A

C

H T

A

B C

4 cm

E

7

10. Name the included angle between AB and AC .

State whether the pairs of figures are congruent. Explain.

Exterior Angles: Find each angle measure.

37. mB ___________________ 38. mPRS ___________________

39. In LMN, the measure of an exterior angle at N measures 99.

1m

3L x

and 2

m3

M x . Find mL, mM, and mLNM. ____________________

40. mE and mG __________________ 41. mT and mV ___________________

42. In ABC and DEF, mA mD and mB mE. Find mF if an exterior

angle at A measures 107, mB (5x 2) , and mC (5x 5) . _______________

43. The angle measures of a triangle are in the ratio 3 : 4 : 3. Find the angle measures of the triangle.

____________________

44. One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle?

___________________

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45. The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle?

_______________________

46. The measure of one of the acute angles in a right triangle is x°. What is the measure of the other acute angle?

_________________________

47. Find mB 48. Find m<ACD

49. Find mK and mJ 50. Find m<P and m<T

Use the figure at the right for problems 1-3.

1. Find m3 if m5 = 130 and m4 = 70.

2. Find m1 if m5 = 142 and m4 = 65.

3. Find m2 if m3 = 125 and m4 = 23.

Use the figure at the right for problems 4-7.

4. m6 + m7 + m8 = _______.

5. If m6 = x, m7 = x – 20, and m11 = 80,

then x = _____.

6. If m8 = 4x, m7 = 30, and m9 = 6x -20,

then x = _____.

7. m9 + m10 + m11 = _______.

For 8 – 12, solve for x.

8.

9.

1 3

5 2 4

6

8

7 10

11

9

120

x°

(5x)°

x° 140°

35°

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4.5 – 4.7 Proving Triangles are congruent Ways to Prove ’s :

SSS Postulate: (side-side-side) Three sides of one are to three sides of a second ,

Given: AS bisects PW ; AWPA

SAS Postulate: (side-angle-side) Two sides and the included angle of one are to two sides

and the included angle of another .

Given: PX bisects AXE; XEAX

ASA Postulate: (angle-side-angle) Two angles and the included side of one are to two angles

and the included side of another .

Given: MHAT

THMA

//

//

AAS Theorem: (angle-angle-side) Two angles and a non-included side of one are to two

angles and a non-included side of another .

Given: CAtsbiUZ sec

ZAUZCUUZ ;

HL Theorem: (hypotenuse-leg) The hypotenuse and leg of one right are to the hypotenuse

and leg of another right .

Given: FCAT

Isosceles FAC with legs ACFA,

CPCTC: Corresponding parts of congruent triangles are congruent

A

P W S

A

X

P

E

A

M

T

H

C

R U Z

A

A

F T C

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∆’s SSS, SAS, ASA, AAS, or HL

State which congruence method(s) can be used to prove the ∆s . If no method applies, write none. All markings must

correspond to your answer.

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Fill in the congruence statement and then name the postulate that proves the ∆s are . If the ∆s are not , write “not possible” in second blank. (Leave first blank

empty) *Markings must go along with your answer**

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#1 Given: USUTSRUTSR ;//; Prove: UVST //

1. USUTSRUTSR ;//; 1. _____________________________

2. 1 4 2. __________________________________________

3. ∆RST ∆TUV 3. __________________________________________

4. 3 2 4. __________________________________________

5. UVST // 5. __________________________________________

#2 Given: D is the midpoint of CBCAAB ; Prove: CD bisects ACB.

1. D is the midpoint of CBCAAB ; 1. _________________________________________

2. DBAD 2. __________________________________________

3. CDCD 3. __________________________________________

4. ∆ACD ∆BCD 4. __________________________________________

5. 1 2 5. __________________________________________

6. CD bisects ACB. 6. __________________________________________

#3 Given: AR≅ AQ; RS ≅ QT Prove: AS ≅ AT

1. AR≅ AQ; RS ≅ QT 1. ________________________

2. <R <Q 2. __________________________________________

3. ARS AQT 3. __________________________________________

4. AS ≅ AT 4. __________________________________________

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Fill in Proofs:

#1

Given: AB CB

AC BD

Prove: Δ ADB Δ CDB

1. AB CB 1. _________________________________________________

2. AC BD 2. _________________________________________________

3. 1 & 2 are right ’s. 3. _________________________________________________

4. 1 2 4. _________________________________________________

5. BD BD 5. _________________________________________________

6. Δ ADB Δ CDB 6. _________________________________________________

#2

Given: AC BD

BD bisects ADC

Prove: AB CB

1. AC BD 1. _________________________________________________

2. 1 & 2 are right ’s 2. _________________________________________________

3. 1 2 3. _________________________________________________

4. BD BD 4. _________________________________________________

5. BD bisects ADC 5. _________________________________________________

6. 3 4 6. _________________________________________________

7. Δ ADB Δ CDB 7. _________________________________________________

8. AB CB 8. _________________________________________________

B

3 4

1 2

D

A C

D

B

3 4

1 2 A C

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Congruent Triangles Proofs

1. Given: SP ; O is the midpoint of PS

Prove: O is the midpoint of RQ

2. Given: ABCD ; D is the midpoint of AB

Prove: CBCA

3. Given: KRSNNRSK //;//

Prove: KRSNNRSK ;

4. Given: MEADMEAD ;//

M is the midpoint AB

Prove: EBDM //

5. BONUS Given: DACDABACAB ;

Prove: BCD is isosceles

7. BONUS Given: PRMRQRPQRM ;

Prove: PQMQ

A B

C

D

S

K

N

R

1

2 3

4

A M B

E D

A

C B

D

Q

R

P

M

P

O

R S

Q

15

8. Given:

DCDE

BDAD

BCAE

Prove: ADCEDB

9. Given: MKAB

B is the midpoint of MK

Prove: yx

10. Given: 21

FMCD

Prove: CD bisects MCF

11. Given: QVPV

QSPS

//

//

Prove: yx

12. Given:

BDAE

CDCE

BCAC

Prove: 21

13. Given:

ABDB

BEBC

BEDB

BCAB

Prove: AD

A B

C

D

E A

B M K

x y

C D

M

F

1

2 S

Q V P

x Y

C

A D E B

1 2

E

A

B

D

C

16

14. Given: D and C are supplementary

B and C are supplementary

BEDFABAD ,

Prove: yx

15. Given: RSTSSKSL ,

Prove: LK

16. Given: RDDABRBA ,

Prove: RAXDBX

17. Given:

ZOYO

ZXZOYXYO

,

Prove: ZXYX

18. Given: GFBCEFCD

CFGECFBD

,

,

Prove: ACF is isosceles

19. Given: BCAB

BD is a median of ABC

Prove: CBDABD

20. Given: PR bisects QPS

PR is an altitude of QPS

Prove: PQS is isosceles

A B

E

C F D

x

y

S

R

K

T

L

B D

A

X

R

Y

O

Z

X A

B

C D E

F

G

B

C

D

A

P

Q

R

S