Advertisements
Advertisements
प्रश्न
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
Advertisements
उत्तर
Given to determine the measure of each of the equal angles of right– angled isosceles triangle
Consider on a right – angled isosceles triangle ABC such that
∠A = 90° and AB = AC
Since, AB = AC ⇒ ∠C = ∠B ……….(1)
[Angles opposite to equal sides are equal] Now,
Sum of angles in a triangle = 180°
∠A + ∠B +∠C = 180°
⇒ 90° + ∠B + ∠B = 180° [ ∴∠A = 90° and ∠B = ∠C ]
⇒ 2∠B = 90°
⇒ ∠B = 45°⇒ ∠C = 45°
∴ ∠B =∠C = 45°
Hence, the measure of each of the equal angles of a right-angled isosceles triangle is 45°.
APPEARS IN
संबंधित प्रश्न
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:
- OB = OC
- AO bisects ∠A
In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC 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°
Which of the following statements are true (T) and which are false (F):
The bisectors of two equal angles of a triangle are equal
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
Fill the blank in the following so that the following statement is true.
If altitudes CE and BF of a triangle ABC are equal, then AB = ....
Fill the blank in the following so that the following statement is true.
In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.
Which of the following statements are true (T) and which are false (F)?
Sum of the three sides of a triangle is less than the sum of its three altitudes.
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.
In the given figure, what is y in terms of x?
In the given figure, the value of x is ______.
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
Which of the following correctly describes the given triangle?
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].
