ABC is a triangle in which altitudes BD and CE to sides AC and AB are – InterviewSolution

InterviewSolution

1.

ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure). Show that i) ΔABD ≅ ΔACE ii) AB = AC i.e., ABC is an isosceles triangle.

Answer»

Given that BD ⊥ AC; CE ⊥ AC

BD = CE

Now in ΔABD and ΔACE

∠ADB = ∠AEC (∵ given 90°)

∠A = ∠A (commori angle)

BD = CE

∴ ΔABD = ΔACE (∵ AAS congruence)

⇒ AB = AC (∵ C.P.C.T)

Discussion

No Comment Found

Related InterviewSolutions

One of the angles of a triangle is 1/2 radian and the other is 99°. What is the third angle in radian measure? 1. \(\dfrac{9\pi - 10}{\pi}\)2. \(\dfrac{90\pi - 100}{7\pi}\)3. \(\dfrac{90\pi - 10}{\pi}\)4. None of the above
If a, b, c are in GP and log a - log 2b, log 2b - log 3c and log 3c - log a are in AP, then a, b, c are the lengths of the sides of a triangle which is1. Acute angle2. Obtuse angled3. Right angles4. Equilateral
One angle of a right angled triangle is 70°. Find the other acute angle.
If the centroid of a triangle formed by (4,x), (y,-5) and (7, 8) is (3, 5), then the values of x and y are respectively1. 2, 122. -12, 133. 12, -24. 13, -2
If perpendicular of a right angled triangle is 8 cm and its area is 20 cm2, the length of base is?1. 20 cm2. 05 cm3. 40 cm4. 08 cm
ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure). Show that i) ΔABD ≅ ΔACE ii) AB = AC i.e., ABC is an isosceles triangle.
What is the minimum data required for constructing a triangle?1. Measure of two angles2. Length of any two sides and measure of their included angle3. Length of two sides4. Measure of one angle and length of one side
AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that (i) ΔDAP ≅ ΔEBP(ii) AD = BE