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 ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD
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°.
ABC is a triangle in which ∠B = 2 ∠C. D is a point on BC such that AD bisects ∠BAC and AB = CD.
Prove that ∠BAC = 72°.
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):
If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.
Which of the following statements are true (T) and which are false (F):
The two altitudes corresponding to two equal sides of a triangle need not be equal.
Fill the blank in the following so that the following statement is true.
In an equilateral triangle all angles are .....
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.
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 ……
ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = \[\frac{1}{2}\] ∠A.
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
In the given figure, if AB ⊥ BC. then x =
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
In the given figure, if l1 || l2, the value of x is
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
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.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
