Download Honors Geometry Unit #4 Lesson #1 Triangle Sum Theorem: The

Honors Geometry
Unit #4 Lesson #1
Triangle Sum Theorem: The sum of the measures of the angles of any triangle is 180°.
Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the
measures of the remote interior angles.
Review of triangle classification and vocabulary:
Classifying Triangles by Their Angles:
 Acute – all angles are acute
 Right – has one right angle
 Obtuse – has one obtuse angle
Classifying Triangles by Their Sides:
 Scalene – all sides have different lengths
 Isosceles – has at least two congruent sides
 Equilateral – all three sides are congruent
A
Vocabulary of an isosceles triangle:
 Vertex – the angle between congruent sides (A)
 Base angles – the two angles that are not the vertex (B and C)
 Legs – the two congruent sides ( AB and AC )
 Base – the side that is not a leg (opposite the vertex) ( BC )
B
Vocabulary of a right triangle:
 Hypotenuse – the side across from the right angle ( AB )
 Legs – the sides adjacent to the right angle ( BC and AC )
A
C
B
C
Honors Geometry
Unit #4 Assignment #1
1. Classify each triangle as acute, right, or obtuse.
a.
42°
37°
b. 1 is complementary to 2.
1
2
2. Are each of the following statements true or false. If they are true, explain why. If they are
false, give a counterexample.
a. Every equilateral triangle is acute.
b. A triangle can have two obtuse angles.
c. A triangle can have two acute exterior angles.
d. Each triangle can have at most one right angle.
3. In DEF, mD = 12x – 6, mE = 5x + 2,and mF = 6x. Classify DEF by its sides and by its
angles.
4. The angles of a triangle are in a ratio of 3:4:5. What is the measure of the largest angle?
5. If m1 = 112° and m7 = 69°, find the measures of the other numbered angles.
7
6
5
3
4
2
1
6. In the diagram the mCAB = 80° and mCBA = 60°. If AE and BD are altitudes, find mC
and mAFB.
C
E
D
F
A
B
7. In the diagram below, mG = 50°. Find mM.
G
M
J
H
8. In DEF, the sum of the measures of D and E is 110°. The sum of the measures of E and
F is 150°. Find the sum of the measures of D and F.
9. The measures of two angles of a triangle are in the ratio of 2:3. If the third angle is 4 degrees
more than the larger of the other two angles, find the measure of an exterior angle at the third
vertex.
10. If mPST = (x + 3y)°, mP = 45°, mR = 2y°, and mPSR = 5x°, find mPST.
P
R
Key:
1.
2.
3.
4.
5.
S
a. obtuse b. right
a. T b. F c. F d. T
right scalene
75°
68°,43°,137°,69°,111°
T
6. 40°,140°
7. 115°
8. 100°
9. 110°
10. 105°