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  • 1

    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

    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

  • 2

    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.

  • 3

    Match the letter of the figure to the correct vocabulary word in Exercises 14.

    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 810, 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?

  • 4

    3. mX __________ 4. BC __________ mA __________

    5. PQ __________ 6. mK __________ t __________

  • 5

    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.

  • 6

    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?

    ___________________

  • 8

    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

  • 9

    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

  • 10

    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.

  • 11

    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**

  • 12

    #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.

  • 13

    Fill in Proofs:

    #1

    Given: AB CB

    AC BD

    Prove: ADB 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. ADB 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.

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