7.5A & 7.5C Similar Figures Review

Front

What are similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal or if the lengths of their corresponding sides are proportional (AA, SSS, or SAS similarity criteria).

Front

What is the formula for finding the missing side of similar figures?

Back

If two figures are similar, the ratio of their corresponding sides is equal to the ratio of their corresponding heights. Use the formula: (side1/side2) = (height1/height2).

Front

If triangle A has sides of 4 cm, 6 cm, and 8 cm, and triangle B has a side of 2 cm, what is the length of the corresponding side in triangle B?

Back

The corresponding side in triangle B is 1 cm.

Front

What is the scale factor in similar figures?

Back

The scale factor is the ratio of the lengths of two corresponding sides of similar figures. It indicates how much one figure has been enlarged or reduced compared to the other.

Front

If two similar triangles have a scale factor of 3:1, and the longer side of the smaller triangle is 4 cm, what is the length of the corresponding side in the larger triangle?

Back

The length of the corresponding side in the larger triangle is 12 cm.

Front

What is the relationship between the areas of two similar figures?

Back

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides.

Front

If the sides of two similar rectangles are in the ratio 2:5, what is the ratio of their areas?

Back

The ratio of their areas is 2^2:5^2, which simplifies to 4:25.

Front

How can you use a mirror to find the height of a tree?

Back

By standing at a distance from the tree and using a mirror on the ground, you can create similar triangles to calculate the height of the tree based on your height and the distance from the tree.

Front

If a triangle has sides measuring 5 cm, 12 cm, and 13 cm, is it a right triangle?

Back

Yes, it is a right triangle because it satisfies the Pythagorean theorem: 5^2 + 12^2 = 13^2.