Advertisements
Advertisements
Questions
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
Solution
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
RELATED QUESTIONS
Prove that the medians of an equilateral triangle are equal.
Prove that each angle of an equilateral triangle is 60°.
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Which of the following statements are true (T) and which are false (F):
If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.
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.
In a ΔABC if ∠A = ∠C , then AB = ......
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 = ....
In a ΔABC, if ∠B = ∠C = 45°, which is the longest side?
In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
In ΔABC, side AB is produced to D so that BD = BC. If ∠B = 60° and ∠A = 70°, prove that: (i) AD > CD (ii) AD > AC
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than the third side.
The angles of a right angled triangle are
Which of the following correctly describes the given triangle?
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 ______.
In ∆PQR, if ∠R > ∠Q, then ______.
If ∆PQR ≅ ∆EDF, then is it true to say that PR = EF? Give reason for your answer
Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC
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].
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
