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1. Refer to the figure. What is the
special name given to the pair
of angles shown by 2 and 6?
2. Refer to the figure. Find m3.
3. Refer to the figure. Find m4.
4. Find the slope of the line that contains the points at (4,
4) and (2, –5).
5. What is the slope of a line that is perpendicular to
the line
• Identify and classify triangles by angles.
• Identify and classify triangles by sides.
• acute triangle
• scalene triangle
• obtuse triangle
• isosceles triangle
• right triangle
• equilateral triangle
• equiangular triangle
Classify Triangles by Angles
A. ARCHITECTURE The triangle truss below is
modeled for steel construction. Use a protractor to
classify ΔJMN, ΔJKO, and ΔOLN as acute,
equiangular, obtuse, or right.
Classify Triangles by Angles
Answer: ΔJMN has one angle with measure greater
than 90, so it is an obtuse triangle. ΔJKO has
one angle with measure equal to 90, so it is a
right triangle. ΔOLN is an acute triangle with all
angles congruent, so it is an equiangular
triangle.
A. ARCHITECTURE The frame of this
window design is made up of many
triangles. Classify ΔABC.
A. acute
B. equiangular
C. obtuse
D. right
A.
B.
C.
D.
A
B
C
D
B. ARCHITECTURE The frame of this
window design is made up of many
triangles. Classify ΔACD.
A. acute
B. equiangular
C. obtuse
D. right
A.
B.
C.
D.
A
B
C
D
C. ARCHITECTURE The frame of this
window design is made up of many
triangles. Classify ΔADE.
A. acute
B. equiangular
C. obtuse
D. right
A.
B.
C.
D.
A
B
C
D
Classify Triangles by Sides
A.
Isosceles triangles have at least two sides congruent.
Answer: ΔUTX and ΔUVX are isosceles.
Classify Triangles by Sides
B.
Scalene triangles have no congruent sides.
Answer: ΔVYX, ΔZTX, ΔVZU, ΔYTU, ΔVWX, ΔZUX,
and ΔYXU are scalene.
A. Which of the following triangles are isosceles?
A. ΔABC and
ΔABD
B. ΔADE and
ΔAEB
C. ΔBED and
ΔACB
D. ΔACD and
ΔACB
1.
2.
3.
4.
A
B
C
D
B. Which of the following triangles is scalene?
A. ΔABE
B. ΔACE
C. ΔADE
D. ΔABD
1.
2.
3.
4.
A
B
C
D
Find Missing Values
ALGEBRA Find d and the measure
of each side of equilateral triangle
KLM if KL = d + 2, LM = 12 – d, and
KM = 4d – 13.
Since ΔKLM is equilateral,
each side has the same length.
So KL = KM.
Substitution
2 = 3d – 13
Subtract d from each side.
Add 13 to each side.
5=d
Divide each side by 3.
Find Missing Values
Next, substitute to find the length of each side.
Answer: For ΔKLM, d = 5 and the measure of each side
is 7.
ALGEBRA Find x and the measure of each side of
equilateral triangle ABC if AB = 6x – 8, BC = 7 + x, and
AC = 13 – x.
A. x = 10 and all sides are 3.
B. x = 6 and all sides are 13.
C. x = 3 and all sides are 10.
D. x = 3 and all sides are 16.
1.
2.
3.
4.
A
B
C
D
Use the Distance Formula
COORDINATE GEOMETRY Find the measures of
the sides of ΔRTS. Classify the triangle by sides.
Use the Distance Formula
Use the distance formula to find the lengths of each side.
Answer:
since all 3
sides have different lengths, ΔRST is scalene.
Find the measures of the sides
of ΔABC. Classify the triangle
by sides.
A. scalene
B. isosceles
C. equilateral
D. cannot be determined
A.
B.
C.
D.
A
B
C
D