Advertisements
Advertisements
प्रश्न
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 = ....
Advertisements
उत्तर
If altitudes CE and BF of a triangle ABC are equal, then
AB A C
Reason: From RHS congruence criterionΔ BEC ≅CFB ⇒∠EBC = ∠FCB⇒∠ABC = ∠ACB⇒ AC=AB
[ ∵Sides opposite to equal angels are equal]
APPEARS IN
संबंधित प्रश्न
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
The vertical angle of an isosceles triangle is 100°. Find its base angles.
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.
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°.
ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Which of the following statements are true (T) and which are false (F):
The bisectors of two equal angles of a triangle are equal
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
Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?
O is any point in the interior of ΔABC. Prove that
(i) AB + AC > OB + OC
(ii) AB + BC + CA > OA + QB + OC
(iii) OA + OB + OC >` 1/2`(AB + BC + CA)
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)?
If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it.
In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find ∠ACD: ∠ADC.
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
In the given figure, x + y =
In the given figure, what is z in terms of x and y?
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
