Similar Shapes

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How to Identify and Name Similar Polygons

You can identify similar polygons by comparing their corresponding angles and sides. As you see in the following figure, quadrilateral WXYZ is the same shape as quadrilateral [more…]

How to Align Similar Polygons

If you get a problem with a diagram of similar polygons that aren’t lined up in the same orientation, consider redrawing one of them so that they’re both aligned in the same way. This may make the problem [more…]

How to Solve a Similar Polygon Problem

Recall that similar polygons are polygons whose corresponding angles are congruent and whose corresponding sides are proportional. The figure below shows similar pentagons, [more…]

How to Prove Triangles Similar Using the AA Theorem

You can use the AA (Angle-Angle) method to prove that triangles are similar. The AA theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles [more…]

How to Prove Triangles Similar with SSS~

You can prove that triangles are similar using the SSS~ (Side-Side-Side) method. SSS~ states that if the ratios of the three pairs of corresponding sides of two triangles are equal, then the triangles [more…]

How to Prove Triangles Similar with SAS~

You can prove that triangles are similar using the SAS~ (Side-Angle-Side) method. SAS~ states that if two sides of one triangle are proportional to two sides of another triangle and the included angles [more…]

How to Use CASTC after Proving Triangles Similar

CASTC is simply an acronym that stands for ‘Corresponding angles of similar triangles are congruent.’ You often use CASTC in a proof immediately after proving triangles similar [more…]

How to Use the Angle-Bisector Theorem

The Angle-Bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides. The following figure illustrates [more…]

How to Solve Problems with the Altitude-0n-Hypotenuse Theorem

In a right triangle, the altitude that’s perpendicular to the hypotenuse has a special property: it creates two smaller right triangles that are both similar to the original right triangle. [more…]

How to Solve Similar Triangle Problems with the Side-Splitter Theorem

You can solve certain similar triangle problems using the Side-Splitter Theorem. This theorem states that if a line is parallel to a side of a triangle and it intersects the other two sides, it divides [more…]

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