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 ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
The vertical angle of an isosceles triangle is 100°. Find its base angles.
Find the measure of each exterior angle of an equilateral triangle.
PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.
Prove that each angle of an equilateral triangle is 60°.
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.
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN.
Which of the following statements are true (T) and which are false (F):
Angles opposite to equal sides of a triangle are equal
Which of the following statements are true (T) and which are false (F):
If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.
In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC
Fill in the blank to make the following statement true.
Difference of any two sides of a triangle is........ than the third side.
If the angles A, B and C of ΔABC satisfy the relation B − A = C − B, then find the measure of ∠B.
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?
In the given figure, if AB ⊥ BC. then x =
In the given figure, what is the value of x?
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
In the given figure, if l1 || l2, the value of x is
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
