Triangle Proportionality Theorem

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.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

How do you determine if two triangles are similar using the AA criterion?

Back

Two triangles are similar if two angles of one triangle are equal to two angles of another triangle.

Front

What is the formula for solving proportions?

Back

If a/b = c/d, then ad = bc.

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).

Front

What is the significance of the Side-Splitter Theorem?

Back

The Side-Splitter Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides into segments that are proportional.

Front

If a triangle has sides of lengths 6, 8, and x, and is similar to another triangle with sides 3, 4, and 5, what is the value of x?

Back

x = 10, since the triangles are similar and the ratio of corresponding sides is 6/3 = 2.

Front

What is the Cross-Multiplication method used for?

Back

Cross-Multiplication is used to solve proportions by multiplying the means and extremes.

Front

If two triangles are similar and the length of one side of the first triangle is 12 and the corresponding side of the second triangle is 8, what is the scale factor?

Back

The scale factor is 12/8 or 3/2.