Exploring Triangle Properties: Medians, Altitudes, and Angle Bisectors

This lesson covers the properties of triangles, focusing on congruence, midpoints, medians, altitudes, and angle bisectors. It explains the characteristics of isosceles triangles and demonstrates how to calculate the perimeter using the Pythagorean theorem. The lesson concludes with a practical example and encourages students to continue learning.

What does it mean for two triangles to be congruent?

• They completely overlap when placed on top of each other.

• They have the same perimeter.

• They have the same area.

• They have the same color.

How are the sides and angles labeled in a triangle?

• Sides with lowercase letters, angles with the same letter opposite the corresponding side.

• Sides with numbers, angles with lowercase letters.

• Sides with symbols, angles with uppercase letters.

• Sides with uppercase letters, angles with numbers.

What is a midpoint segment in a triangle?

• A line segment connecting two points and parallel to the opposite side.

• A line segment connecting the midpoints of the base.

• A line segment connecting two midpoints of the sides.

• A line segment connecting a vertex to the opposite side.

What is a median in a triangle?

• A line segment connecting a vertex to the opposite side at a right angle.

• A line segment connecting the midpoints of two sides.

• A line segment connecting two vertices.

• A line segment connecting a vertex to the midpoint of the opposite side.

What is an altitude in a triangle?

• A line segment connecting the midpoints of two sides.

• A line segment connecting a vertex to the opposite side at a right angle.

• A line segment connecting two vertices.

• A line segment connecting a vertex to the midpoint of the opposite side.

What is an angle bisector in a triangle?

• A line segment connecting the midpoints of two sides.

• A line segment connecting a vertex to the midpoint of the opposite side.

• A line segment connecting two vertices.

• A line segment that divides an angle into two equal parts.

What is unique about the median, altitude, and angle bisector in an isosceles triangle?

• They are all parallel to each other.

• They do not exist.

• They are all the same line if they come from the vertex opposite the unequal side.

• They are all different lines.

What is the sum of all interior angles in any triangle?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

If the base of an isosceles triangle is 12 cm and the median to the base is 8 cm, what is the length of each half of the base?

• 8 cm

• 6 cm

• 12 cm

• 4 cm

Using the Pythagorean theorem, if one leg of a right triangle is 6 cm and the other leg is 8 cm, what is the length of the hypotenuse?

• 6 cm

• 12 cm

• 8 cm

• 10 cm