Advertisements
Advertisements
प्रश्न
In the given figure, what is y in terms of x?
विकल्प
- \[\frac{3}{2}x\]
- \[\frac{4}{3}x\]
- 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
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.
ABC is a triangle in which ∠B = 2 ∠C. D is a point on BC such that AD bisects ∠BAC and AB = CD.
Prove that ∠BAC = 72°.
Which of the following statements are true (T) and which are false (F):
The measure of each angle of an equilateral triangle is 60°
Fill the blank in the following so that the following statement is true.
In a ΔABC if ∠A = ∠C , then AB = ......
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than the third side.
Which of the following statements are true (T) and which are false (F)?
Difference of any two sides of a triangle is equal to the third side.
Fill in the blank to make the following statement true.
The sum of any two sides of a triangle is .... than the third side.
Fill in the blank to make the following statement true.
If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
In the given figure, if AB ⊥ BC. then x =
In the given figure, if BP || CQ and AC = BC, then the measure of x is
In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =
In the given figure, if l1 || l2, the value of x is
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.
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.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
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
ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In ∆ABD and ∆ACD,
AB = AC (Given)
∠B = ∠C (Because AB = AC)
and ∠ADB = ∠ADC
Therefore, ∆ABD ≅ ∆ACD (AAS)
So, ∠BAD = ∠CAD (CPCT)
What is the defect in the above arguments?
[Hint: Recall how ∠B = ∠C is proved when AB = AC].
