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Standard VII
Mathematics
Question

Which of the following statements is true?
  1. In an isosceles triangle, the angles opposite to equal sides are equal
  2. If the hypotenuse and an acute angle of one right angled triangle is equal to the hypotenuse and the corresponding acute angle of another triangle, then the triangles are congruent.
  3. The bisector of the vertical angle of an isosceles triangle bisects the base at right angles
  4. All of the above

A
In an isosceles triangle, the angles opposite to equal sides are equal
B
The bisector of the vertical angle of an isosceles triangle bisects the base at right angles
C
If the hypotenuse and an acute angle of one right angled triangle is equal to the hypotenuse and the corresponding acute angle of another triangle, then the triangles are congruent.
D
All of the above
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Solution
Verified by Toppr

Option A is true

In an isosceles triangle, two sides are equal.
Theorem: the angles opposite to equal sides are also equal

option B is true
It can be proved by SAS congruency rule.

option C is true

Yes, this is called AAS congruency Rule.





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Q1

Question 104

State whether the statement is True or False.

If the hypotenuse and an acute angle of one right-angled triangle are equal to the hypotenuse and an acute angle of another right-angled triangle, then the triangles are congruent.

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Q2
Which of the following statements are true and which of them are false?

(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two figures have equal areas, they are congruent.
(iv) If two triangles are equal in area, they are congruent.
(v) If two sides and one angle of a triangle are equal to the corresponding two sides and angle of another triangle, the triangle are congruent.
(vi) If two angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent.
(vii) If three angles of a triangle are equal to the corresponding angles of another triangle then the triangles are congruent.
(viii) If the hypotenuse and an acute angle of a right triangle are equal to the hypotenuse and the corresponding acute angle of another right triangle then the triangle are congruent.
(ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.
(x) If two triangles are congruent then their corresponding sides and their corresponding angles are congruent.
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Q3

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 the triangle need not be equal

(viii) If any two sides of a right triangle are respectively equal to two sides of another 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 to the hypotenuse and a side of the other triangle.

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Q4
Assertion : If the hypotenuse and an acute angle of one right triangle is equal to the hypotenuse and corresponding acute angle of another right triangle, then those two Δs are congruent.
Reason : By RHS property, the two right Δs are congruent.
Which of the following statements is correct?

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Q5
Consider the following statements relating to the congruency of two right triangles.
(1) Equality of two sides of one triangle with any two sides of the second makes the triangle congruent.
(2) Equality of the hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangle congruent.
(3) Equality of the hypotenuse and an acute angle of one triangle with the hypotenuse and an angle of the second respectively makes the triangle congruent.
Of these statements:
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