Ratios, Proportions and Similar Polygons

A fruit bowl contains 5 apples and 7 oranges. What is the ratio of oranges to the total pieces of fruit?

The sides of a triangle are in the extended ratio 3:5:8, and its perimeter is 48 cm. What is the length of the shortest side?

In the proportion 4/7 = 12/21, the means are 4 and 21.

In a proportion, the product of the extremes equals the product of the ______.

Solve for x in the following proportion: 3/x = 9/15

What is the arithmetic mean of the numbers 4 and 16?

What is the geometric mean of 5 and 20?

If a/b = c/d, then a/d = c/b is a valid transformation according to the properties of proportions.

Given that x/y = 5/2, which of the following is equivalent based on the properties of proportions?

Two similar triangles have corresponding side lengths of 4 and 12. What is the scale factor of the smaller triangle to the larger triangle?

If two polygons are congruent, what is their scale factor?

If two triangles are similar, their corresponding angles are proportional.

If ΔPQR ~ ΔXYZ, then ∠P is congruent to ∠______.

Given ΔABC ~ ΔDEF, AB = 8, DE = 12, and BC = 6, find the length of EF.

ΔABC has angle measures ∠A = 50° and ∠B = 70°. ΔXYZ has angle measures ∠X = 50° and ∠Y = 70°. Are the triangles similar? If so, by which theorem?

What is the minimum amount of information needed to prove that two triangles are similar using Angle-Angle Similarity (AA~)?

Side-Side-Angle (SSA) is a valid method for proving triangle similarity.

If two triangles have two pairs of sides whose lengths are in the same proportion, and the included angles are congruent, then the triangles are similar by ______ similarity.

In ΔABC and ΔXYZ, AB/XY = BC/YZ = CA/ZX = 2. By which similarity postulate or theorem are the triangles similar?

Given ΔABC and ΔDEF, where AB = 4, BC = 6, DE = 6, EF = 9, and ∠B ≅ ∠E. Are the triangles similar? If so, by what theorem?

If the geometric mean of two numbers is 6, and one of the numbers is 4, what is the other number?

When an altitude is drawn to the hypotenuse of a right triangle, the two smaller triangles formed are similar to each other, but not similar to the original triangle.

In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the ______ mean of the lengths of the two segments.

In a right triangle with the altitude drawn to the hypotenuse, if one segment of the hypotenuse is 4 and the other is 9, what is the length of the altitude?

In a right triangle, the altitude to the hypotenuse divides the hypotenuse into segments of length 3 and 12. What is the length of the shorter leg of the original triangle?

What transformation changes the size of a figure?

A dilation with a scale factor of 0.7 is an enlargement.

To dilate a figure by a scale factor of k using the origin as the center of dilation, the transformation is (x, y) -> (______, ______).

A triangle with vertices A(2, 4), B(6, 2), and C(4, 8) is dilated by a factor of 2. What are the coordinates of vertex A'?

A square has a side length of 3 cm. It is enlarged to a square with a side length of 12 cm. What is the scale factor of the enlargement?

Two similar figures have a scale factor of 5:3. What is the ratio of their areas?

If two similar triangles have perimeters in the ratio of 2:3, then their areas are in the ratio of 4:9.

If the scale factor for the area of two polygons is 9:4, then the scale factor for their side lengths is ______.

A 6m high pole casts a shadow of 4m. At the same time, a nearby tree casts a shadow of 12m. How high is the tree?

You are creating a scale model of a building that is 50 feet tall. If you want your model to be 2 feet tall, what is the scale factor you should use?

The Side-Splitter Theorem applies when a line intersects a triangle side at its midpoint.

The Side-Splitter Theorem states that if a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides ______.

In ΔABC, DE is parallel to BC, AD = 4, DB = 6, and AE = 5. Find EC.

Three parallel lines intersect two transversals. The segments on one transversal are 6 and 9, and the corresponding segment on the second transversal adjacent to the '6' segment is 4. What is the corresponding segment on the second transversal to the '9' segment?

If a ray bisects an angle of a triangle, what relationship is established?

If a ray bisects an angle of a triangle, it always divides the opposite side into two equal segments.

If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are ______ to the lengths of the other two sides.

In ΔPQR, PS bisects ∠P, QS = 3, SR = 5, and PQ = 6. Find PR.