BA is a transversal that intersects the two parallel lines A'C' and AC, hence the corresponding angles BA'C' and BAC are congruent.

Find the length y of BC' and the length x of A'A. In the triangle ABC shown below, A'C' is parallel to AC.

Similar Triangles Problems with Solutions Problems 1

The two triangles have two sides whose lengths are proportional and a congruent angle included between the two sides.

Since the lengths of the sides including the congruent angles are given, let us calculate the ratios of the lengths of the corresponding sides.

Show that triangles ABC and A'BC', in the figure below, are similar. If an angle of a triangle is congruent to the corresponding angle of a second triangle, and the lengths of the two sides including the angle in one triangle are proportional to the lengths of the corresponding two sides in the second triangle, then the two triangles are similar.

The lengths of the corresponding sides are proportional and therefore the two triangles are similar.

We now calculate the ratios of the lengths of the corresponding sides.ĪB / PQ = 2, BC / QR = 2 and CA / RP = 2.

Since we know the coordinates of the vertices, we can find the length of the sides of the two triangles.

Let us first plot the vertices and draw the triangles.

If the three sides of a triangle are proportional to the corresponding sides of a second triangle, then the triangles are similar. Since the two triangles have two corresponding congruent angles, they are similar.

Since A'C' is parallel to AC, angles BA'C' and BAC are congruent.

What can you say about triangles ABC and A'BC'? Explain your answer.

Let ABC be a triangle and A'C' a segment parallel to AC. If two angles in a triangle are congruent to the two corresponding angles in a second triangle, then the two triangles are similar.

Two triangles ABC and A'B'C' are similar if the three angles of the first triangle are congruent to the corresponding three angles of the second triangle and the lengths of their corresponding sides are proportional as follows. Also examples and problems with detailed solutions are included. Similar Triangles Examples and Problems with Solutionsĭefinitions and theorems related to similar triangles are discussed using examples.

Aa similarity postulate