Interior and Exterior Angles of Triangles

Interior and Exterior Angles of

Polygons

TEKS: Geom.6D Verify theorems about the relationships in triangles. Including proof of the Pythagorean Theorem, the sum of the interior

angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems.

LO: SWBAT verify theorems about the relationships in triangles including proof of the
Triangle Sum Theorem and apply these relationships to determine the sum of interior
and exterior angles of a polygon.

DOL: Given a set of problems, students will verify theorems about the relationships in
triangles including proof of the Triangle Sum Theorem and apply these relationships to determine the sum of interior and exterior angles of a polygon in at least 4 of 5
questions.

Vocabulary

Triangle Sum Theorem

Def: all interior angles of a triangle equal to 180 degrees.

If you are given 2 out the 3 interior angles,
then you can use the substitution property
to find the 3rd angle.

Ex.

Given: A = 35°
B = 67°

Find: angle C

Math Response

Solve for x

Type answer here

Correct Answer: 58

Deg^°

Rad

Math Response

Solve for x

Type answer here

Correct Answer: 33

Deg^°

Rad

Open Ended

Solve for f and find the missing angle measure.

Answer Notation:

f=

a=

Exterior Angle Theorem

When we trace ∠1 and ∠2, both

angles will fit in ∠3. Which means

that∠1 + ∠2 = ∠3.

Def: The measure of an exterior angle in a triangle is equal to the sum of the two remote interior angles.

Exterior Angle Theorem

Statement

Reasons

∠2 ≅∠4

∠1 ≅∠3

∠1 + ∠2 ≅ ∠3 + ∠4

Math Response

Solve for n

Type answer here

Correct Answer: 55

Deg^°

Rad

Math Response

Solve for z

Type answer here

Correct Answer: 29

Deg^°

Rad

Open Ended

Solve for d and find the missing interior angle.

Answer notation:

d=

a=

Assignment and DOL Time