Advertisements
Advertisements
Question
State the two properties which are necessary for given two triangles to be similar.
Solution
The two triangles are similar if and only if
1. The corresponding sides are in proportion.
2. The corresponding angles are equal.
APPEARS IN
RELATED QUESTIONS
State which pair of triangles in the following figure are similar. Write the similarity criterion used by you for answering the question, and also write the pairs of similar triangles in the symbolic form:
In the given figure, D is a point on hypotenuse AC of ΔABC, DM ⊥ BC and DN ⊥ AB, Prove that:
(i) DM2 = DN.MC
(ii) DN2 = DM.AN
In ΔABC, AL and CM are the perpendiculars from the vertices A and C to BC and AB respectively. If AL and CM intersect at O, prove that:
(i) ΔOMA and ΔOLC
(ii) `"OA"/"OC"="OM"/"OL"`
A ladder 10m long reaches the window of a house 8m above the ground. Find the distance of the foot of the ladder from the base of the wall.
In the given figure, ∠AMN = ∠MBC = 76° . If p, q and r are the lengths of AM, MB and BC respectively then express the length of MN of terms of P, q and r.
It is given that ΔDEF ~ ΔRPQ. Is it true to say that ∠D = ∠R and ∠F = ∠P? Why?
In figure, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD.
A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3 m, find how far she is away from the base of the pole.
In the above figure, seg AC and seg BD intersect each other in point P. If `("AP")/("CP") = ("BP")/("DP")`, then complete the following activity to prove ΔABP ∼ ΔCDP.
Activity: In ΔABP and ΔCDP
`("AP")/("CP") = ("BP")/("DP")` ......`square`
∴ ∠APB ≅ `square` ......Vertically opposite angles
∴ `square` ∼ ΔCDP ....... `square` test of similarity.
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ΔPQR show that ΔABC ~ ΔPQR.