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
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
The vertical angle of an isosceles triangle is 100°. Find its base angles.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC.
Prove that each angle of an equilateral triangle is 60°.
Which of the following statements are true (T) and which are false (F):
Angles opposite to equal sides of a triangle are equal
Which of the following statements are true (T) and which are false (F):
The measure of each angle of an equilateral triangle is 60°
Fill the blank in the following so that the following statement is true.
Sides opposite to equal angles 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 = ....
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.
Fill in the blank to make the following statement true.
If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.
In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In the given figure, what is z in terms of x and y?
In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =
Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be ______.
M is a point on side BC of a triangle ABC such that AM is the bisector of ∠BAC. Is it true to say that perimeter of the triangle is greater than 2 AM? Give reason for your answer.
Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
