Download Warm-Up Exercises

Warm-Up
Exercises
Bell Work
Classify each angle as acute, obtuse, or right.
1. 90º
2. 72º
3. 116º
4. How do you know that
~ 2?
1=
2
1
Warm-Up
Exercises
Notes
Warm-Up1Exercises
EXAMPLE
Classify triangles by sides and by angles
Classify the triangular shape of the support beams in
the diagram by its sides and by measuring its angles.
Warm-Up2Exercises
EXAMPLE
Classify a triangle in a coordinate plane
Classify PQO by its sides.
Then determine if the triangle
is a right triangle.
SOLUTION
Warm-Up
Exercises
GUIDED
PRACTICE
1.
for Examples 1 and 2
Draw an obtuse isosceles triangle and
an acute scalene triangle.
B
Q
A
C
obtuse isosceles triangle
R
P
acute scalene triangle
Warm-Up
Exercises
Notes
Definitions
Interior Angles:
Exterior Angles:
Warm-Up
Exercises
Notes
Theorems:
Triangle Sum Theorem: The sum of the measures of the interior
angles of a 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 two
nonadjacent interior angles.
Warm-Up
Exercises
Notes
http://www.geogebratube.org/student/m99847
Proof of the Triangle Sum Theorem
Warm-Up3Exercises
EXAMPLE
Find an angle measure
Find m JKM.
Warm-Up
Exercises
Notes
Corollary to the Triangle Sum Theorem:
The acute angles of a right triangle are complementary.
Note: a corollary is a statement that can be proved easily using
the theorem.
Warm-Up
Exercises
Notes
Proof of Corollary to the Triangle Sum Theorem
Warm-Up4Exercises
EXAMPLE
Find angle measures from a verbal description
ARCHITECTURE
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.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 3 and 4
4. Find the measure of each interior angle of
ABC,
where m A = x ° , m B = 2x° , and m C = 3x°.
x
2x
3x
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 3 and 4
5. Find the measures of the acute
angles of the right triangle in
the diagram shown.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
1. Graph ABC with vertices A(0, 6), B(– 4, – 1) and
C(4, – 1). Classify it by its sides. Then determine if
it is a right triangle.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
2. Find x. Then classify the triangle by its angles.
3. Find the measure of exterior angle shown.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
4. Find x and y.
Warm-Up
Exercises
For Tomorrow
Homework
HW: 4.1 (pg. 212-213) #1-6,12,14,18,31,44-47,50