Advertisements
Advertisements
Question
In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:
ΔABD ∼ ΔCBE
Solution
In ΔABD and ΔCBE
∠ADB = ∠CEB = 90°
∠ABD = ∠CBE ....(Common angle)
Hence, by using the AA similarity criterion,
ΔABD ∼ ΔCBE
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, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:
ΔPDC ∼ ΔBEC
In the following figure, AB || QR. Find the length of PB.
In the following Figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm and AD = 4 cm, find CD.
In the following Figure, DE || BC such that AE = (1/4) AC. If AB = 6 cm, find AD.
The sides of certain triangles are given below. Determine which of them right triangles are.
1.4cm, 4.8cm, 5cm
The sides of certain triangles are given below. Determine which of them right triangles are.
1.6cm, 3.8cm, 4cm
In the given figure, DE║BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and EC = (3x + 19) cm. Find the value of x.
The corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm2, find the area of the larger triangle.
Two triangles DEF an GHK are such that ∠D = 48° and ∠H = 57° . If ΔDEF ∼GHK then find the measures of ∠F
In the given figure, value of x(in cm) is
If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true?
It is given that ΔDEF ~ ΔRPQ. Is it true to say that ∠D = ∠R and ∠F = ∠P? Why?
In figure, BD and CE intersect each other at the point P. Is ΔPBC ~ ΔPDE? Why?
If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of ∆ABC.
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.
□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
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 the given figure, ∠ADC = ∠BCA; prove that ΔACB ∼ ΔADC. Hence find BD if AC = 8 cm and AD = 3 cm.
