Advertisements
Advertisements
प्रश्न
Find the measure of each exterior angle of an equilateral triangle.
Advertisements
उत्तर
Given to find the measure of each exterior angle of an equilateral triangle consider an
equilateral triangle ABC.
We know that for an equilateral triangle
AB = BC = CA and
`∠ABC =∠BCA =∠CAB=180^@/3=60^@` .......1
Now,
Extend side BC to D, CA to E and AB to F.
Here
BCD is a straight line segment
`⇒∠BCD = Straight angle 180^@`
`∠BCA+∠ACD=180^@`
`⇒60^@+∠ACD=180^@`
Similarly, we can find ∠FAB and ∠FBC also as `120^@` because ABC is an equilateral
triangle
`∴∠ACD =∠EAB =∠FBC =120^@`
Hence, the median of each exterior angle of an equilateral triangle is `120^@`
APPEARS IN
संबंधित प्रश्न
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
Which of the following statements are true (T) and which are false (F) :
If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
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 ……
In a ΔABC, if ∠B = ∠C = 45°, which is the longest side?
Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than twice the median drawn to the third side.
Fill in the blank to make the following statement true.
In a right triangle the hypotenuse is the .... side.
Write the sum of the angles of an obtuse triangle.
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
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 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.
In a triangle ABC, D is the mid-point of side AC such that BD = `1/2` AC. Show that ∠ABC is a right angle.
