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TODAY IN GEOMETRY…
STATs on Ch. 3 Test
Learning Target: 4.1 Classify Triangles and find measures of their angles
Independent Practice
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HOW DID YOU “SHAPE” UP??Results for ALL of my Geometry classes:
GRADE NUMBER OF STUDENTS WHO TOOK THE CH.9 TEST (36 pts.)
1ST PERIOD 3RD PERIOD 5TH PERIOD 6TH PERIOD TOTAL
A 15 22 15 23 75B 3 2 3 2 10C 4 3 4 2 13D 1 1 1 0 3F 2 2 1 1 6
Avg. 31.28 32.57 32.46 33.98 32.57
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CLASSIFYING TRIANGLES BY SIDES AND ANGLES
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CLASSIFYING TRIANGLES BY SIDES:
TRIANGLE # of congruent sides example
SCALENE
ISOSCELES
EQUILATERAL
0
2
3
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ACUTE ANGLE: An angle whose measure is between 0 and 90 degrees
RIGHT ANGLE: An angle whose measure is 90 degrees
OBTUSE ANGLE: An angle whose measure is between 90 and 180 degrees
REVIEW ANGLE VOCABULARY:
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CLASSIFYING TRIANGLES BY ANGLES:
TRIANGLE Type of Angle example
ACUTE
RIGHT
OBTUSE
EQUIANGULAR
3 acute angles1 right angle
1 obtuse angle
3 congruent angles
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Classify △ABC by its sides. Determine if the triangle is a right triangle.
B
A
C
1. Use the distance formula to find the length of each side.
2. Calculate slope to determine right angles.
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B(-1, 2)
A(0, 0)
1. Use the distance formula to find the length of each side.
C(6, 3)
None of the sides of the triangle have the same length so this triangle is SCALENE.
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𝐴𝐵=2−0−1−0
=2−1
=−21
B(-1, 2)
A(0, 0)
2. Calculate slope to determine right angles.C(6, 3)
The slope of and are negative reciprocals so , therefore this is a RIGHT SCALENE TRIANGLE.
𝐵𝐶=3−26−(−1)
=17
𝐴𝐶=3−06−0
=36=12
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INTERIOR VS EXTERIOR ANGLES
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1
23
Interior Angles: Exterior Angles:
4
5
6
7
89
Extend sides of a polygon to find exterior angles.
Interior angles are found inside the polygon.
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TRIANGLE SUM THEOREM:
ADDING ALL THE INSIDE ANGLES
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TRIANGLE SUM THEOREM: The sum of the measures of the interior angles of a triangle is .
1
32
∠𝟏+∠𝟐+∠𝟑=𝟏𝟖𝟎 °
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2 𝑥
𝑥−6
Find x.
The sum of the interior angles of a triangle is
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EXTERIOR ANGLE THEOREM:
MEASURE OF THE OUTSIDE IS TWO OF THE INSIDE
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EXTERIOR ANGLE THEOREM: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
1
32
∠𝟏+∠𝟐=∠𝟒4
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𝑥
Find x and y.
Using the Exterior Angles Theorem:
𝑦
95
130 Using the Triangle Sum Theorem:
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𝑥 Find x.
70 2 𝑥−5Using the Exterior Angles Theorem:
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3 𝑥 Find x and y.
Using the Exterior Angles Theorem:
𝑦40 5 𝑥−10Using the Triangle Sum Theorem:
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HOMEWORK #1:
Pg. 221: 1-26, 32, 35-37