Equilateral Triangle Theorem

Q. If all the angles of a triangle are equal then it is said to be __.

1. a isosceles triangle
2. a right angled triangle
3. a scalene triangle
4. an equilateral triangle

Q. All the sides in an equilateral triangle are:

1. distinct
2. 1 cm
3. equal
4. 6 cm

Q. All the angles in an equilateral triangle is equal to?

1. 30 degrees
2. 90 degrees
3. 60 degrees
4. 45 degrees

Q. If 3 sides of one triangle are equal to the three sides of another triangle, then the two triangles are .

1. congruent by SSS
2. congruent by SAA
3. congruent by SAS
4. congruent by SSA

Q. All three angles of a triangle always add upto .

1. ${180}^{\circ }$
2. ${90}^{\circ }$
3. ${360}^{\circ }$
4. ${270}^{\circ }$

Q. If $\Delta ABC$ $\cong$ $\Delta DEF$ by SSS congruence, then, match the corresponding equal sides.

1. DE
2. EF
3. FD

Q. If two angles are congruent and one of them measure 60 degrees, then the other measures ______.

1. 60 degrees
2. 50 degrees
3. 70 degrees
4. 80 degrees

Q. The normals at three points $P,Q,R$ of the parabola $y^2=4ax$ meet in $(h,k)$, the centroid of triangle $PQR$ lies on

1. $y=-a$
2. $x=a$
3. $y=0$
4. $x=0$

Q. Algebraic sum of the slopes of normals at co-normal points is zero.

1. True
2. False

Q. Which of the following is the equation of circle through co-normal points of parabola $y^2=4ax$ ?

1. $x^2+y^2-(3a+h)x-(\frac{k}{3})y=0$
2. $x^2+y^2-(2a+h)x-(\frac{k}{2})y=0$
3. $x^2+y^2-(3a+k)x-(\frac{h}{3})y=0$
4. $x^2+y^2-(2a+k)x-(\frac{h}{2})y=0$