Theorem 7.2 : Angles opposite to equal sides of an isosceles triangle are equal.
Text Solution
Verified by Experts
In `/_\BAD` and `/_\CAD`
`AB=AC` given
`/_BAD=/_CAD` by construction
`AD=AD` common
By SAS congruence rule,
`/_\BAD` and `/_\CAD` are congruent.
Thus,
...
Topper's Solved these Questions
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 7.3|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 7.4|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 7.1|1 Videos
LINES AND ANGLES
NCERT ENGLISH|Exercise Exercise 6.1|6 Videos
NUMBER SYSTEMS
NCERT ENGLISH|Exercise EXERCISE 1.4|2 Videos
Similar Questions
Explore conceptually related problems
Theorem 7.3 : The sides opposite to equal angles of a triangle are equal.
Which of the following statements are true (T) and which are false (F): Side opposite to equal angles of a triangle may be unequal. Angle opposite to equal sides of a triangle are equal. The measure of each angle of an equilateral triangle is 60^0 If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. The bisectors of two equal angles of a triangle are equal. If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. The two altitudes corresponding to two equal sides of a triangle need not be equal. If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent. 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.
Fill in the blanks in the following so that each of the following statements is true. (i) Sides opposite to equal angles of a triangle are ....... (ii) Angle opposite to equal sides of a triangle are ....... (iii) In an equilateral triangle all angles are ....... (iv) In a A B C if /_A=/_C , then A B=\ ..... (v) If altitudes C E\ a n d\ B F of a triangle A B C are equal, then A B= ........ (vi) In an isosceles triangle A B C with A B=A C , if B D\ a n d\ C E are its altitudes, then B D is .......... C E . (vii) In right triangles A B C\ a n d\ D E F , if hypotenuse A B=E F and side A C=D E , then A B C\ ~= ....
Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.
Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.
Find the measures of each of the two equal angles of an isosceles right-angled triangle.
Theorem 7.4 (SSS congruence rule) : If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3c m//sdot How fast is the area decreasing when the two equal sides are equal to the base?
The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?
The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3c m//sdot How fast is the area decreasing when the two equal sides are equal to the base?