Advertisements
Advertisements
Question
Which of the following statements are true (T) and which are false (F):
The two altitudes corresponding to two equal sides of a triangle need not be equal.
Advertisements
Solution
False (F)
Reason: Since two sides are equal, the triangle is an isosceles triangle.
⇒ The two altitudes corresponding to two equal sides must be equal.
APPEARS IN
RELATED QUESTIONS
In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.

In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
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.
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):
The measure of each angle of an equilateral triangle is 60°
Fill the blank in the following so that the following statement is true.
In an equilateral triangle all angles are .....
In a ΔABC, if ∠B = ∠C = 45°, which is the longest side?
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)?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
Fill in the blank to make the following statement true.
The sum of any two sides of a triangle is .... than the third side.
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, what is z in terms of x and y?

In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then

In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.
It is given that ∆ABC ≅ ∆FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.

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].
