Advertisements
Advertisements
प्रश्न
Fill the blank in the following so that the following statement is true.
In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.
Advertisements
उत्तर
In an isosceles triangle ABC with AB AC, if BD and CE are its altitudes, then BD
is equal to CE
Reason: Since angles opposite to equal sides are equal, so
∠ABC=∠ ACB
⇒∠EBC=∠ DCB
So, by ASA congruence criterion
ΔEBC ≅ ΔDCB
⇒CE = BD [Corresponding parts of congruent
triangles are equal]
APPEARS IN
संबंधित प्रश्न
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
Prove that the medians of an equilateral triangle are equal.
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
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.
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°.
Fill the blank in the following so that the following statement is true.
In a ΔABC if ∠A = ∠C , then AB = ......
In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC
Which of the following statements are true (T) and which are false (F)?
Sum of the three sides of a triangle is less than the sum of its three altitudes.
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.
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.
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
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.
Find all the angles of an equilateral triangle.
