Which of the following is true for Isosceles right angled triangle?

One right angle

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Two other equal angles always

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Two equal sides

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None of these

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Solution

The correct options are
A One right angle
C Two other equal angles always
D Two equal sides
A right triangle has one right angle and an isosceles triangle has two equal sides and two other angles equal.
So an Isosceles right triangle has one right angle , two equal sides and two other equal angles.
Option $A, B$ and $C$ are correct.

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Q. What is the area of an isosceles right angled triangle of equal sides 16 cm each?

Question 2

Match the following
$\begin{matrix} M e a s u r e o f T r i a n g l e & T y p e s o f t r i a n g l e 3 s i d e s o f e q u a l l e n g t h & S c a l e n e 2 s i d e s o f e q u a l l e n g t h & I s o s c e l e s r i g h t a n g l e A l l s i d e s a r e o f d i f f e r e n t l e n g t h & O b t u s e a n g l e 3 a c u t e a n g l e s & R i g h t a n g l e 1 r i g h t a n g l e & E q u i l a t e r a l 1 o b t u s e a n g l e & A c u t e a n g l e 1 r i g h t a n g l e w i t h t w o s i d e s o f e q u a l L e n g t h & I s o s c e l e s \end{matrix}$

Question 2 Match the following $\begin{matrix} Measure of Triangle & Types of triangle 3 sides of equal length & Scalene 2 sides of equal length & Isosceles right angle All sides are of different length & Obtuse angle 3 acute angles & Right angle 1 right angle & Equilateral 1 obtuse angle & Acute angle 1 right angle with two sides of equal Length & Isosceles \end{matrix}$

Which of the following statements are true (T) and which are false (F):

(i) Sides opposite to equal angles of a triangle may be unequal.

(ii) Angles opposite to equal sides of a triangle are equal.

(iii) The measure of each angle of an equilateral triangle is 60°.

(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

(v) The bisectors of two equal angles of a triangle are equal.

(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.

(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.

(viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.

(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal equal to the hypotenuse and a side of the other triangle.

Q. For an isosceles right-angled triangle having each of equal sides 'a', we have
I.

Area = \frac{1}{2} a^{2}

II.

Perimeter = (2 + \sqrt{2}) a

III. Hypotenuse = 2a
Which of the following is true?
(a) I only
(b) II only
(c) I and II
(d) I and III

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