Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.
Similarity
140 Likes

Question

Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.

KnowledgeBoat · Accepted Answer

Let two similar triangles be △ABC and △PQR. We know that when triangles are similar ratio of corresponding sides are equal. By property of ratio i.e., if then each ratio = . So, Since, AB + BC + AC = Perimeter of △ABC and PQ + QR + PR = Perimeter of △PQR. So, Hence, proved.

Mathematics

Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.

Similarity

Related Questions

In the figure (3) given below, ∠ PQR = ∠ PRS. Prove that triangles PQR and PRS are similar. If PR = 8 cm, PS = 4 cm, calculate PQ.

In the adjoining figure, ABC is a triangle in which AB = AC. P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC. Prove that BM × NP = CN × MP.

In the figure (1) given below, AB, EF and CD are parallel lines. Given that AB = 15 cm, EG = 5 cm, GC = 10 cm and DC = 18 cm. Calculate
(i) EF (ii) AC

Mathematics

Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.

Similarity

Related Questions

In the figure (3) given below, ∠ PQR = ∠ PRS. Prove that triangles PQR and PRS are similar. If PR = 8 cm, PS = 4 cm, calculate PQ.

In the adjoining figure, ABC is a triangle in which AB = AC. P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC. Prove that BM × NP = CN × MP.

In the figure (1) given below, AB, EF and CD are parallel lines. Given that AB = 15 cm, EG = 5 cm, GC = 10 cm and DC = 18 cm. Calculate(i) EF (ii) AC

In the figure (1) given below, AB, EF and CD are parallel lines. Given that AB = 15 cm, EG = 5 cm, GC = 10 cm and DC = 18 cm. Calculate
(i) EF (ii) AC