# Methods of Characterization

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MCHS

MATHEMATICS III

SUMMER 2013

Name: ___________________________| Date: ____________|

ACTIVITY NO. 15

CONGRUENT TRIANGLES, SPECIAL SEGMENTS, ISOSCELES TRIANGLES,INEQUALITY

I.If enough information is given:a) state the postulate or theorem that verifies the congruence of the triangles; and

b) write the congruent statement. (10 points)

L

K

F

E

B

C

1.A

D

a) ________________b) ________________| 2.G

J

H

a) ________________b) ________________| 3.N

M

a) ________________b) ________________|

Q

P

4.R

U

T

S

a) ________________b) ________________| V

5.Y

W

X

a) ________________b) ________________| |

II. Encircle P if the given set of numbers is possible lengths of the sides of a triangle, otherwise encircle ~P. (4 points)

P| ~P| 1.| {6, 8, 9}|

P| ~P| 2.| {8, 15, 16}|

P| ~P| 3.| {12, 17, 29}|

P| ~P| 4.| {10, 24, 26}|

III. If two sides of a triangle have the following measures, find the range of possible measures for the third side (x). (2 points)

1. 12, 23

2. 8, 31

IV. Use <, >, =, or CND (cannot be determined) to compare the following quantities. (5 points)

1.| m3| _____| 1

2

3

4

5

6

7

8

9

10

11

12

m8|

2.| m4| _____| m6|

3.| m1| _____| m11|

4.| m12| _____| m2|

5.| m1 + m10| _____| m2 + m11|

V. Problem Solving. Show complete solutions and write answer on the spaces provided. (19 points)

1. If COW PIG, mC = 55, mI = 55, what is the mW? (1 point)

mW = __________

2. CAT DOG. If CA = x + 4, OG = 3x, DG = 4x – 6 and the perimeter of CAT is 30 cm, solve for the value of x and the length of CT. (3 points)

Eq’n for x: ____________________________

x = ____________

CT = ___________

3. In HRE, HS is an angle bisector, RY is an altitude and OE is a median. (8 points)

a) If mEHR = 8x – 14 and mSHR is x + 14, find x and mEHS.

Eq’n for x: ________________________________

H

O

R

S

E

Y

x = ___________

mEHS = ____________

b) If HO = 4y + 1 and RO = 8y – 7, find y and HR.

Eq’n for y: ________________________________

y = ___________

HR = ____________

c) If mYHR = 2z + 6 and mHRY = 5z, find z.

Eq’n for z: ________________________________

z = ___________

4. In MEW, MW = ME. If mE = 5x – 9 and mM = 8x, solve for x and the m1. (3 points) 1

W

Eq’n for x: ________________________________

x = ___________

E

M

m1 = ____________

5. In MAC, mA = 53, mM = 7x – 8 and mC = 8x. Solve for x, determine the measure of the largest angle and arrange the sides of MAC from least to greatest. (4 points)

Eq’n for x: ________________________________

x = ___________

measure of largest angle = __________________

arrangement of MA, AC, MC: ____________________

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