Unit 5 Review: Relationships in Trianlges

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If a triangle has sides of lengths 7 and 12, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than |7 - 12| and less than 7 + 12, so the range is: 5 < x < 19.

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

Front

What is an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

Back

This represents the range of possible lengths for a side of a triangle, ensuring it satisfies the Triangle Inequality Theorem.

Front

What is the relationship between the sides of a triangle and the angles opposite those sides?

Back

In a triangle, the larger the side, the larger the angle opposite that side.

Front

How do you determine if a triangle can exist with given side lengths?

Back

Use the Triangle Inequality Theorem: the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is the significance of the median in triangle geometry?

Back

Medians divide a triangle into two smaller triangles of equal area.