Triangle Properties and Angle Relationships

Mrs. Apia presents lesson 13 on the angle sum of a triangle, explaining the angle sum theorem which states that the sum of the interior angles of a triangle is always 180 degrees. The lesson includes exploratory challenges to demonstrate this theorem using parallel lines and transversals, and students are guided through naming angles and understanding angle relationships. The lesson concludes with a substitution proof to reinforce the theorem.

What is the essential question for Lesson 13?

• How do you find the perimeter of a triangle?

• Why are triangles important in geometry?

• What two pieces of knowledge help prove the sum of interior angles of a triangle?

• How do you calculate the area of a triangle?

According to the angle sum theorem, what is the sum of the interior angles of any triangle?

• 270 degrees

• 360 degrees

• 180 degrees

• 90 degrees

Which of the following is true about the angles in an acute, obtuse, and right triangle?

• All types of triangles have an angle sum of 180 degrees.

• Only acute triangles have an angle sum of 180 degrees.

• Only right triangles have an angle sum of 180 degrees.

• They all have different angle sums.

What is the correct way to name an angle in a triangle?

• Using the first and last letters of the triangle

• Using only the vertex letter

• Using three letters with the vertex as the middle letter

• Using any three letters in any order

What type of angles are formed when a transversal cuts through parallel lines?

• Vertical angles

• Corresponding and alternate interior angles

• Supplementary angles

• Complementary angles

In the substitution proof, which angles are replaced to show the sum of 180 degrees?

• Angles 1 and 2

• Angles 3 and 4

• Angles 2 and 3

• Angles 1 and 4, and angles 2 and 5

What is the purpose of using substitution in the angle sum theorem proof?

• To determine the type of triangle

• To calculate the perimeter of the triangle

• To show that the sum of the interior angles is 180 degrees

• To find the area of the triangle

In the exploratory challenge, what is the role of the straight angle?

• To measure the height of the triangle

• To prove the sum of the interior angles is 180 degrees

• To determine the type of triangle

• To find the base of the triangle

What is a transversal in the context of parallel lines?

• A line that is tangent to a circle

• A line that is perpendicular to another line

• A line that intersects two or more lines

• A line that is parallel to another line

How do alternate interior angles relate to parallel lines?

• They are always complementary

• They are equal in measure

• They are always supplementary

• They are never equal