Advertisements
Advertisements
प्रश्न
In the given figure, S is a point on side QR of ΔPQR such that ∠QPR = ∠PSR. Use this information to prove that PR2 = QR × SR.
उत्तर
Given: ∠QPR = ∠PSR
In ΔQPR and ΔPSR,
∠QRP ≅ ∠PRS ......[Common angle]
∠QPR ≅ ∠PSR ......[Given]
So, according to the AA similarity criterion,
ΔQPR ∼ ΔPSR
∴ `(QR)/(PR) = (PR)/(SR)` .......[C.S.S.T.]
⇒ QR × SR = PR2
Hence proved.
APPEARS IN
संबंधित प्रश्न
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 a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.
The sides of certain triangles are given below. Determine which of them right triangles are.
1.6cm, 3.8cm, 4cm
State the AAA-similarity criterion
In the given figure, value of x(in cm) is
In triangle PQR and MST, ∠P = 55°, ∠Q = 25°, ∠M = 100° and ∠S = 25°. Is ∆QPR ~ ∆TSM? Why?
Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? 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.
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.
If in two triangles ABC and PQR, `(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`, then ______.
In ΔABC, seg XY || side AC. If 2AX = 3BX and XY = 9, then find the value of AC.
□ABCD is a parallelogram. Point P is the midpoint of side CD. seg BP intersects diagonal AC at point X, then prove that: 3AX = 2AC
In ΔABC, AP ⊥ BC, BQ ⊥ AC. If AP = 7, BQ = 8 and BC = 12, then find AC.
In the given figure below, `(AD)/(AE) = (AC)/(BD)` and ∠1 = ∠2, Show that ΔBAE ∼ ΔCAD.
If ΔABC ~ ΔDEF and ∠A = 47°, ∠E = 83°, then ∠C is equal ______.
Diagonals of a trapezium PQRS intersect each other at the point O, PQ || RS and PQ = 3 RS. Find the ratio of the areas of triangles POQ and ROS.
