Proportions in Triangles

Front

What is a proportion in the context of triangles?

Back

A proportion in triangles refers to the equality of two ratios, often used to compare the lengths of corresponding sides of similar triangles.

Front

What is the Triangle Proportionality Theorem?

Back

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

Front

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

Back

The corresponding sides of similar triangles are in proportion, meaning the ratios of their lengths are equal.

Front

How do you find the missing length in a proportion?

Back

To find the missing length in a proportion, set up a ratio and cross-multiply to solve for the unknown.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 cm and side DE is 8 cm, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Front

What is the significance of the Side-Splitter Theorem?

Back

The Side-Splitter Theorem states that if a line intersects two sides of a triangle, it divides those sides proportionally.

Front

How can proportions be used to solve for unknown variables in triangles?

Back

Proportions can be set up using the lengths of corresponding sides to create equations that can be solved for unknown variables.

Front

What is the relationship between the angles of similar triangles?

Back

In similar triangles, corresponding angles are equal.

Front

If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

Back

It is a right triangle, as it follows the Pythagorean theorem (3^2 + 4^2 = 5^2).