Advertisements
Advertisements
Question
State which pair of triangles in the given 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:
Solution
In ΔABC and ΔPQR
`("AB")/("QR") = 2/4 = 1/2`
`("BC")/("RP") = 2.5/5 = 1/2`
`("CA")/("PQ") = 3/6 = 1/2`
`("AB")/("QR") = ("BC")/("RP") = ("CA")/("PQ")`
∴ ΔABC ~ ΔQRP ...[By SSS similarity criterion]
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 following figure, `("QR")/("QS") = ("QT")/("PR")` and ∠1 = ∠2. Show that ΔPQS ~ ΔTQR.
S and T are point on sides PR and QR of ΔPQR such that ∠P = ∠RTS. Show that ΔRPQ ∼ ΔRTS.
E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ΔABE ∼ ΔCFB.
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 the following figure, XY || BC. Find the length of XY.
State the two properties which are necessary for given two triangles to be similar.
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.
In the given figure, value of x(in cm) is
In the given figure, PQ = 24 cm, QR = 26 cm ∠PAR = 90°, PA = 6 cm, and AR = 8 cm, the degree measure of ∠QPR is ______.
In ABC, DE || AB. If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to ______.
It is given that ∆ABC ~ ∆EDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.
It is given that ΔABC ~ ΔDFE, ∠A =30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, the following is true ______.
In figure, l || m and line segments AB, CD and EF are concurrent at point P. Prove that `(AE)/(BF) = (AC)/(BD) = (CE)/(FD)`.
A tangent ADB is drawn to a circle at D whose centre is C. Also, PQ is a chord parallel to AB and ∠QDB = 50°. Find the value of ∠PDQ.
In ΔABC, AP ⊥ BC, BQ ⊥ AC. If AP = 7, BQ = 8 and BC = 12, then find AC.
Which of the following is NOT a similarity criterion of traingles?
In ΔABC, DE || AB. If AB = a, DE = x, BE = b and EC = c. Then x expressed in terms of a, b and c is ______.
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.