Unit 8 Review: Triangle Proportionality & Triangle Inequality Th

Front

What is Triangle Proportionality?

Back

Triangle Proportionality states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

What is the Triangle Inequality Theorem?

Back

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

Front

If a triangle has sides of lengths 5, 12, and 13, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 5 + 12 > 13, 5 + 13 > 12, and 12 + 13 > 5.

Front

What is the formula to find the width of a river using similar triangles?

Back

Width = (Height of object) * (Width of object) / (Height of river) using the properties of similar triangles.

Front

List the conditions under which three lengths can form a triangle.

Back

The lengths must satisfy the Triangle Inequality Theorem: a + b > c, a + c > b, and b + c > a.

Front

What is the significance of the longest side in a triangle?

Back

The longest side of a triangle is always opposite the largest angle.

Front

How do you determine if a set of lengths can form a triangle?

Back

Check if the sum of the two shorter lengths is greater than the longest length.

Front

What is a proportional relationship in triangles?

Back

A proportional relationship in triangles means that the ratios of corresponding sides are equal.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (Pythagorean theorem).