1. 4.14.1 Apply Triangle Sum Properties
Bell Thinger
1. 90º
ANSWER right
2. 72º
Classify each angle as acute, obtuse, or right.
ANSWER acute
3. 116º
ANSWER obtuse

2. 4.1

3. 4.1

4. 4.1Example 1
SOLUTION
The triangle has a pair of congruent
sides, so it is isosceles. By
measuring, the angles are 55°, 55°,
and 70° . It is an acute isosceles
triangle.
Classify the
triangular shape of the support beams
in the diagram by its sides and by
measuring its angles.
Support Beams

5. 4.1Example 2
SOLUTION
STEP 1 Use the distance formula to find the side lengths.
Classify PQO by its sides.
Then determine if the triangle
is a right triangle.
OP = y2
– y1( )2
x2
– x1( )2
+ = 2 – 0( )2
(– 1 ) 0( )2
+–
= 5 ≈ 2.2
OQ = y2
– y1( )2
x2
– x1( )2
+
2
= – 0( )6 0( )2
+– 3
= 45 ≈ 6.7

6. 4.1Example 2
PQ = y2
– y1( )2
x2
– x1( )2
+ 3 – 2( )2
6( )2
+–= (– 1 )
= 50 ≈ 7.1
STEP 2 Check for right angles.
The slope of OP is
2 – 0
– 2 – 0
= – 2.
The slope of OQ is 3 – 0
6 – 0
=
2
1 .
Therefore, PQO is a right scalene triangle.
ANSWER
1
The product of the slopes is – 2
2
= – 1,
so OP OQ and POQ is a right angle.

7. 4.1Guided Practice
1. Draw an obtuse isosceles triangle and an acute
scalene triangle.
obtuse isosceles triangle
B
A C
acute scalene triangleP
Q
R
SAMPLE ANSWER

8. 4.1
2. Triangle ABC has the vertices A(0, 0), B(3, 3), and
C(–3, 3). Classify it by its sides. Then determine if
it is a right triangle.
isosceles; right triangle
ANSWER
Guided Practice

9. 4.1

10. 4.1
Find m JKM.
Example 3
SOLUTION
STEP 1 Write and solve an equation to find the value
of x.
Apply the Exterior Angle Theorem.(2x – 5)° = 70° + x°
Solve for x.x = 75
The measure of JKM is 145°.ANSWER
STEP 2 Substitute 75 for x in 2x – 5 to find m JKM.
2x – 5 = 2 75 – 5 = 145.

11. 4.1

12. 4.1
The tiled staircase
shown forms a right triangle. The
measure of one acute angle in the
triangle is twice the measure of the other.
Find the measure of each acute angle.
Example 4
ARCHITECTURE
SOLUTION
First, sketch a diagram of the situation.
Let the measure of the smaller acute
angle be x°. Then the measure of the
larger acute angle is 2x°. The Corollary
to the Triangle Sum Theorem states that
the acute angles of a right triangle are
complementary.

13. 4.1Example 4
Use the corollary to set up and solve an equation.
Corollary to the Triangle Sum Theoremx° + 2x° = 90°
Solve for x.x = 30
So, the measures of the acute angles are 30° and
2(30°) = 60 .
ANSWER

14. 4.1Guided Practice
Find the measure of 1 in the diagram shown.3.
The measure of 1 in the diagram is 65 .ANSWER

15. 4.1
4. Find the measure of each interior angle of  ABC,
where m A = x°, m B = 2x°, and m C = 3x°.
m A = 30°, m B = 60°, m C = 90°ANSWER
5. Find the measures of the acute
angles of the right triangle in
the diagram shown.
26° and 64°ANSWER
Guided Practice

16. 4.1Exit Slip
1. Find x. Then classify the triangle
by its angles.
22; acuteANSWER
2. Find the measure of the exterior
angle shown.
104°ANSWER

17. 4.1Exit Slip
3. Find x and y.
82, 58ANSWER

18. 4.1
Homework
Pg 229-232
#14, 18, 32, 36, 40