Advertisements
Advertisements
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.
Advertisements
उत्तर
△ABC is an isosceles triangle.
∴ AB = AC
∠ACB = ∠ABC ...[Angles opposite to equal sides of a △ are equal]
∠BCE = ∠CBF
Now, in △BEC and △CFB
∠BCE = ∠CBF ...[Proved above]
∠BEC = ∠CFB ...[Each 90°]
BC = CB ...[Common]
∴ △BEC ≅ △CFB ...[By AAS congruence]
So, BE = CF ...[By Corresponding parts of congruent triangles]
APPEARS IN
संबंधित प्रश्न
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:
- OB = OC
- AO bisects ∠A
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
Fill the blank in the following so that the following statement is true.
If altitudes CE and BF of a triangle ABC are equal, then AB = ....
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, side AB is produced to D so that BD = BC. If ∠B = 60° and ∠A = 70°, prove that: (i) AD > CD (ii) AD > AC
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 three altitudes of a triangle is ..... than its perimeter.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In the given figure, if AB ⊥ BC. then x =
In the given figure, if l1 || l2, the value of x is
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
If ∆PQR ≅ ∆EDF, then is it true to say that PR = EF? Give reason for your answer
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? 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
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].
