Transcript Lesson 4-1 PowerPoint

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Lesson 4-1 Classifying Triangles
Lesson 4-2 Angles of Triangles
Lesson 4-3 Congruent Triangles
Lesson 4-4 Proving Congruence–SSS, SAS
Lesson 4-5 Proving Congruence–ASA, AAS
Lesson 4-6 Isosceles Triangles
Lesson 4-7 Triangles and Coordinate Proof
Example 1 Classify Triangles by Angles
Example 2 Classify Triangles by Sides
Example 3 Find Missing Values
Example 4 Use the Distance Formula
OBJECTIVE: To identify and classify triangles by
angles (2.9.8D) (M8.C.1.1)
ARCHITECTURE The triangular truss below is
modeled for steel construction. Classify
JMN, JKO, and OLN as acute, equiangular, obtuse,
or right.
Answer:
JMN has one angle with measure greater than 90, so it
is an obtuse triangle.
JKO has one angle with measure equal to 90, so it is a
right triangle.
OLN is an acute triangle with all angles congruent, so it
is an equiangular triangle.
ARCHITECTURE The frame of this window design is
made up of many triangles. Classify ABC, ACD, and
ADE as acute, equiangular, obtuse, or right.
Answer: ABC is acute.
ACD is obtuse.
ADE is right.
Identify the isosceles triangles in the figure if
Isosceles triangles have at least two sides congruent.
Answer: UTX and UVX are isosceles.
Identify the scalene triangles in the figure if
Scalene triangles have no congruent sides.
Answer: VYX, ZTX, VZU, YTU, VWX,
ZUX, and YXU are scalene.
Identify the indicated triangles in the figure.
a. isosceles triangles
Answer: ADE, ABE
b. scalene triangles
Answer: ABC, EBC, DEB, DCE, ADC, ABD
ALGEBRA Find d and the measure of each side of
equilateral triangle KLM if
and
Since KLM is equilateral,
each side has the same
length. So
Substitution
Subtract d from each side.
Add 13 to each side.
Divide each side by 3.
Next, substitute to find the length of each side.
Answer: For KLM,
and the measure of
each side is 7.
ALGEBRA Find d and the measure of each side of
equilateral triangle
if
and
Answer:
COORDINATE GEOMETRY Find the measures of the
sides of RST. Classify the triangle by sides.
Use the distance formula to find the lengths of each side.
Answer:
; since all 3 sides
have different lengths, RST is scalene.
Find the measures of the sides of ABC. Classify the
triangle by sides.
Answer:
; since all 3 sides
have different lengths, ABC is scalene.
Guided Practice
Determine whether each of the following
statements is always, sometimes, or
never true. Explain.
1. Equiangular triangles are also acute?
Always, equiangular triangles have 3 acute angles.
2. Right triangles are acute.
Never, right triangles have one right angle and
acute triangles have all acute angles.
Click the mouse button or press the
Space Bar to display the answers.
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