Advertisements
Advertisements
प्रश्न
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 ______.
पर्याय
`("ac")/"b"`
`("ac")/("b" + "c")`
`("ab")/"c"`
`("ab")/("b" + "c")`
उत्तर
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 `underlinebb((ac)/(b + c))`
Explanation:
In ΔCDE and ΔCAB
∠C = ∠C ...[Common]
∠1 = ∠2 ...[Corresponding angles as DE || AB]
ΔCDE ∼ ΔCAB ...[By AA rule]
`("DE")/("AB") = ("CE")/("BC")` ...[Sides of similar triangles]
`x/"a" = "c"/("b" + "c")`
x = `("ac")/("b" + "c")`
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, PA, QB and RC are each perpendicular to AC. Prove that `1/x+1/z=1/y`
The sides of certain triangles are given below. Determine which of them right triangles are.
7cm, 24cm, 25cm
In the given figure, value of x(in cm) is
In the figure, if DE∥BC, AD = 3cm, BD = 4cm and BC= 14 cm, then DE equals ______.
In figure, BD and CE intersect each other at the point P. Is ΔPBC ~ ΔPDE? 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 a triangle PQR, N is a point on PR such that QN ⊥ PR. If PN . NR = QN2, prove that ∠PQR = 90°.
In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are ______.
If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, can you say that the two triangles will be similar? Why?
