# Methods of Characterization

Topics: Triangle, Congruence, Angle Pages: 5 (456 words) Published: May 21, 2013
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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: ____________________