TODAY IN GEOMETRY… STATs on Ch. 3 Test Learning Target: 4.1 Classify Triangles and find measures...

TODAY IN GEOMETRY…

STATs on Ch. 3 Test

Learning Target: 4.1 Classify Triangles and find measures of their angles

Independent Practice

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

CLASSIFYING TRIANGLES BY SIDES AND ANGLES

CLASSIFYING TRIANGLES BY SIDES:

TRIANGLE # of congruent sides example

SCALENE

ISOSCELES

EQUILATERAL

0

2

3

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:

CLASSIFYING TRIANGLES BY ANGLES:

TRIANGLE Type of Angle example

ACUTE

RIGHT

OBTUSE

EQUIANGULAR

3 acute angles1 right angle

1 obtuse angle

3 congruent angles

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.

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.

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

INTERIOR VS EXTERIOR ANGLES

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.

TRIANGLE SUM THEOREM:

ADDING ALL THE INSIDE ANGLES

TRIANGLE SUM THEOREM: The sum of the measures of the interior angles of a triangle is .

1

32

∠𝟏+∠𝟐+∠𝟑=𝟏𝟖𝟎 °

2 𝑥

𝑥−6

Find x.

The sum of the interior angles of a triangle is

EXTERIOR ANGLE THEOREM:

MEASURE OF THE OUTSIDE IS TWO OF THE INSIDE

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

𝑥

Find x and y.

Using the Exterior Angles Theorem:

𝑦

95

130 Using the Triangle Sum Theorem:

𝑥 Find x.

70 2 𝑥−5Using the Exterior Angles Theorem:

3 𝑥 Find x and y.

Using the Exterior Angles Theorem:

𝑦40 5 𝑥−10Using the Triangle Sum Theorem:

HOMEWORK #1:

Pg. 221: 1-26, 32, 35-37