Advertisements
Advertisements
प्रश्न
In the given figure, what is y in terms of x?
पर्याय
- \[\frac{3}{2}x\]
- \[\frac{4}{3}x\]
- x
\[\frac{3}{4}x\]
Advertisements
उत्तर
In the given figure, we need to find y in terms of x
Now, using the property, “an exterior angle of the triangle is equal to the sum of the two opposite interior angles”, we get
In ΔABC
ext∠ACD = ∠CAB + ∠CBA
ext∠ACD = x + 2x
ext∠ACD =3x ..........(1)
Similarly, in ΔOCD
ext∠AOD = ∠OCD + ∠CDO
3y = ∠OCD + y (using 1)
3y - y = 3x
2y = 3x
`y = 3/2 x`
Thus, `y = 3/2x `
APPEARS IN
संबंधित प्रश्न
In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD
Prove that the medians of an equilateral triangle are equal.
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC.
Which of the following statements are true (T) and which are false (F) :
If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
Fill the blank in the following so that the following statement is true.
In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……
In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
In ΔABC, side AB is produced to D so that BD = BC. If ∠B = 60° and ∠A = 70°, prove that: (i) AD > CD (ii) AD > AC
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = \[\frac{1}{2}\] ∠A.
In the given figure, for which value of x is l1 || l2?
In the given figure, if BP || CQ and AC = BC, then the measure of x is
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
The angles of a right angled triangle are
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC
