Advertisements
Advertisements
Question
In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:
ΔPDC ∼ ΔBEC
Solution
In ΔPDC and ΔBEC
∠PDC = ∠BEC = 90°
∠PCD = ∠BCE ...(Common angle)
Hence, by using the AA similarity criterion,
ΔPDC ∼ ΔBEC
RELATED QUESTIONS
In the following figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB.
S and T are point on sides PR and QR of ΔPQR such that ∠P = ∠RTS. Show that ΔRPQ ∼ ΔRTS.
In the following figure, if ΔABE ≅ ΔACD, show that ΔADE ∼ ΔABC.
In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:
ΔAEP ∼ ΔADB
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 a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.
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"`
The sides of certain triangles are given below. Determine which of them right triangles are.
7cm, 24cm, 25cm
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.
It is given that ΔDEF ~ ΔRPQ. Is it true to say that ∠D = ∠R and ∠F = ∠P? Why?
In figure, if ∠1 = ∠2 and ΔNSQ ≅ ΔMTR, then prove that ΔPTS ~ ΔPRQ.
In figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then, ∠PBA is equal to ______.
In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are ______.
□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 the given figure, ΔLMN is similar to ΔPQR. To find the measure of ∠N, complete the following activity.
Given: ΔLMN ∼ ΔPQR
Since ΔLMN ∼ ΔPQR, therefore, corresponding angles are equal.
So, ∠L ≅ `square`
⇒ ∠L = `square`
We know, the sum of angles of a triangle = `square`
∴ ∠L + ∠M + ∠N = `square`
Substituting the values of ∠L and ∠M in equation (i),
`square` + `square` + ∠N = `square`
∠N + `square` = `square`
∠N = `square` – `square`
∠N = `square`
Hence, the measure of ∠N is `square`.
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.
ABCD is a trapezium with AD ∥ BC and AD = 4 cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB = 1/2, then BC = ______.
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.
