Download Honors Geometry Unit #4 Lesson #2 Isosceles Triangle Theorem

Honors Geometry
Unit #4 Lesson #2
Isosceles Triangle Theorem: The legs of an isosceles triangle are congruent iff the angles opposite them
are congruent.
Midline Theorem: The segment jointing the midpoints of two sides of a triangle is
a. parallel to the third side
and
b. half as long as the third side.
Honors Geometry
Unit #4 Assignment #2
1. Are each of the following statements true or false. If they are true, explain why. If they are
false, give a counterexample.
a. If C is the right angle in right ABC, then A is complementary to B.
b. Exterior angles are always obtuse.
c. If M and N are midpoints in the diagram below, then AMN  ABC.
A
M
N
B
C
2. Sketch and label isosceles XYZ with base YZ .
a. Name the vertex angle.
b. Name the legs.
c. Which sides are congruent?
d. Which angles are congruent?
3. Find the measures of the numbered angles in each figure.
a.
b.
48°
32°
1
2
c.
d.
53°
3
4
10
7
49°
8
5
6
21°
9
4. In ΔXYZ, X  Z. If YZ  2 x  2 , XZ  13x  6 , and XY  6 x  2 , find x and the perimeter
of ΔXYZ.
5. In GHJ, GH  GJ , mH = 10x + 15, and mJ = 7x +3. Classify GHJ by its sides and by its
angles.
6. In a right triangle, the measure of one acute angle is 10° more than three times the measure of the
other. What is the measure of the smallest angle of the triangle?
7. Find m1 in the diagram below.
19°
(2x2 + 38)°
(10x +67)° 1
8. X, Y, and Z are midpoints of the sides of the triangle. Find the perimeter of XYZ below. D and
E are midpoints.
6
X
Y
8
Z
20
9. Graph ABC with vertices A(-5,2), B(7,6), and C(-1,-6).
a. Find the midpoints of AC and BC . Label them M and N respectively.
b. Find the slope of MN and the slope of AB .
c. Find MN and AB.

d. Find the equation of MN .
10. Solve for x and y.
A
2x+y
D
3x+4y
E
4y
B
x+2y+27
C
Answer Key:
1. a. T b. F c. T
2. a. X b. XY and XZ c. XY and XZ d. Y and Z
3. a. m1 = 58° b. m2 = 66° c. m3 = m4 = 78°; m5 = 131° d. m6 = 69°;
m7 = 21°; m8 = 79.5°; m9 = 100.5°; m10 = 21°
4. x = 1 and P = 15
5. Isosceles right
6. 20°
7. 14°
8. 12
1
9. a. (-3,-2) and (3,0) b. 1/3 and 1/3 c. MN = 2 10 ; AB = 4 10 d. y  x  1
3
10. x = 3; y = 2