Post on 22-Jun-2015
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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