4.1 4.1 Apply Triangle Sum Properties Bell Thinger 1. 90º ANSWER right 2. 72º assify each angle as acute, obtuse, or right. ANSWER acute 3. 116º ANSWER obtuse
Jun 22, 2015
4.14.1 Apply Triangle Sum PropertiesBell Thinger
1. 90º
ANSWER right
2. 72º
Classify each angle as acute, obtuse, or right.
ANSWER acute3. 116º
ANSWER obtuse
4.1
4.1
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
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( )2x2 – x1( )2 + = 2 – 0( )2(– 1 ) 0( )2 +–
= 5 ≈ 2.2
OQ = y2 – y1( )2x2 – x1( )2 + 2= – 0( )6 0( )2 +– 3
= 45 ≈ 6.7
4.1Example 2
PQ = y2 – y1( )2x2 – x1( )2 + 3 – 2( )26( )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
=21 .
Therefore, PQO is a right scalene triangle.
ANSWER
1The product of the slopes is – 2
2 = – 1,
so OP OQ and POQ is a right angle.
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
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
4.1
4.1
Find mJKM.
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 2Substitute 75 for x in 2x – 5 to find m∠ JKM.
2x – 5 = 2 75 – 5 = 145.
4.1
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.
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
4.1Guided Practice
Find the measure of 1 in the diagram shown.3.
The measure of 1 in the diagram is 65°.ANSWER
4.1
4. Find the measure of each interior angle of ABC, where mA = x°, mB = 2x°, and mC = 3x°.
mA = 30°, mB = 60°, mC = 90°ANSWER
5. Find the measures of the acute angles of the right triangle in the diagram shown.
26° and 64°ANSWER
Guided Practice
4.1Exit Slip
1. Find x. Then classify the triangle by its angles.
22; acute ANSWER
2. Find the measure of the exterior angle shown.
104°ANSWER
4.1Exit Slip
3. Find x and y.
82, 58 ANSWER
4.1
Homework
Pg 229-232#14, 18, 32, 36, 40