Download Warm-Up Exercises

Warm-Up Exercises
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
EXAMPLE
2Exercises
a triangle
a coordinate
Example
1Classify
(a): Found
on pagein
208
in the book plane
Classify PQO by its sides.
Then determine if the triangle
is a right triangle.
STEP 1 Use the distance formula to find the side lengths.
Warm-Up2Exercises
EXAMPLE
Classify a triangle in a coordinate plane
STEP 2 Check for right angles.
for Examples 1 and 2
Warm-Up
Exercises
Example 1 (b)
GUIDED
PRACTICE
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.
Warm-Up
Try onExercises
your own!
A triangle has the given vertices. Graph the triangle and classify it
By its sides. Then determine if it is a right triangle.
A (2, 3), B (6, 3), C (2, 7)
Warm-Up Exercises
Important
Theorems
THEOREM 4.1: Triangle Sum Theorem
The sum of the measures of the interior angles
of a triangle is 180°.
THEOREM 4.2: 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
EXAMPLE
3Exercises
Example
2Find
(a) Found
onmeasure
page 209
an angle
Find m
JKM.
STEP 1 Write and solve an equation to find the value
of x.
STEP 2 Plug it in! Plug it in!
More Examples
of Using Triangle Angle Sum Theorem and
Warm-Up
Exercises
Exterior Angle Theorem
Find the value of x. Then classify the triangle by its angles.
1.
2.
Warm-Up
Exercises
Try these
for
onExamples
your own!3 and 4
GUIDED
PRACTICE
1. Find the measure of
1 in the diagram shown.
2. Find the value of x and then find the measure of each angle.
3. Find the measure of each interior angle of
ABC,
where m A = x ° , m B = 2x° , and m C = 3x°.
Warm-Up ExercisesCOROLLARY
Corollary: A statement that can be proved
easily using a theorem.
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are
complementary.
Warm-Up4Exercises
EXAMPLE
FindExample
angle measures
3: Page from
210 a verbal description
Step 1: Use the corollary to set up and solve an equation.
Warm-Up
ExercisesTry for
Examples
on your
own! 3 and 4
GUIDED
PRACTICE
Find the measures of the acute
angles of the right triangle in
the diagram shown.
What is the measure of the obtuse angle
formed between the staircase and a segment
extending from the horizontal leg?
A
2x
B
x
C
Q