Advertisements
Advertisements
प्रश्न
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
Advertisements
उत्तर
Given that ABC is a right angled triangle such that ∠A = 90° and AB = AC Since,
AB = AC ⇒ ΔABC is also isosceles
∴ We can say that ΔABC is right angled isosceles triangle
⇒ ∠C=∠B and ∠A=90° ................(1)
Now, we have
Sum of angled in a triangle =180°
⇒ ∠A+∠B+∠C=180°
⇒ 90°+∠B+∠B=180° [∵ From (1)]
⇒ 2∠B=180°-90°
⇒`∠B=(90°)/2=45°`
∴ ∠B=∠C=45°
APPEARS IN
संबंधित प्रश्न
ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
Show that the angles of an equilateral triangle are 60° each.
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°
Find the measure of each exterior angle of an equilateral triangle.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Fill the blank in the following so that the following statement is true.
In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……
Which of the following statements are true (T) and which are false (F)?
Difference of any two sides of a triangle is equal to the third side.
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.
Write the sum of the angles of an obtuse triangle.
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
It is given that ∆ABC ≅ ∆FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
In ∆PQR, if ∠R > ∠Q, then ______.
If ∆PQR ≅ ∆EDF, then is it true to say that PR = EF? Give reason for your answer
In the following figure, D and E are points on side BC of a ∆ABC such that BD = CE and AD = AE. Show that ∆ABD ≅ ∆ACE.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
Find all the angles of an equilateral triangle.
