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
In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
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.
Prove that the medians of an equilateral triangle are equal.
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
The vertical angle of an isosceles triangle is 100°. Find its base angles.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.
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.
Angle opposite to equal sides 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.
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.
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.
Fill in the blank to make the following statement true.
In a right triangle the hypotenuse is the .... side.
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
In the given figure, the value of x is ______.
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
It is given that ∆ABC ≅ ∆FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
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)
