Geometry — Quiz 2

Questions in this quiz (10)

1. Rectangle PQRS has a diagonal of 10 units, and one of its sides measures 6 units. What is the perimeter, in units, of the rectangle?

   • 64
   • 14
   • 28
   • 36

2. A hot air balloon is tethered to the ground with a rope that is 60 meters long. If the angle formed between the rope and the ground is $$47^\circ$$, which of the following is closest to the vertical distance, in meters, from the balloon to the ground? (Assume the rope is taut and the ground is level.)

   • 47
   • 60
   • 44
   • 50

3. In triangle XYZ, side XY = YZ, and side XZ is extended to point W. If angle YZW measures 110°, find the number of degrees in angle Y.

   • $$60^\circ$$
   • $$140^\circ$$
   • $$70^\circ$$
   • $$40^\circ$$

4. In parallelogram WXYZ, angle W measures $$70^\circ$$. What is the sum of angle X and angle Z?

   • $$220^\circ$$
   • $$180^\circ$$
   • $$250^\circ$$
   • $$290^\circ$$

5. The vertex angle of an isosceles triangle is $$q$$ degrees. How many degrees are in one of the base angles?

   • $$\frac{90 - q}{3}$$
   • $$180 - q$$
   • $$90 - q$$
   • $$\frac{180 - q}{2}$$

6. In a circle with center $$P$$, the measure of arc $$AB = 104$$ degrees. How many degrees are there in angle $$PBA$$?

   • 66
   • 38
   • 52
   • 76

7. Given the following figure where O is the center of the circle. Calculate the measure of angle $$\angle EFG$$.

   • $$55^\circ$$
   • $$35^\circ$$
   • $$145^\circ$$
   • $$72.5^\circ$$

8. Identify true statements.(a) The ratio of a pair of corresponding altitudes of two similar triangles is equal to the ratio of any pair of corresponding sides.(b) The ratio of the areas of two similar triangles is equal to the ratio of a pair of corresponding sides.(c) All isosceles right triangles are similar.(d) All equilateral triangles are similar.

   • a, d
   • a, c, d
   • a, b, d
   • b, c, d

9. Two quadrilaterals $$ABCD$$ and $$A_1B_1C_1D_1$$ satisfy:$$\angle A = \angle A_1,\quad \angle B = \angle B_1,\quad \angle C = \angle C_1,\quad \angle D = \angle D_1.$$Are the quadrilaterals similar?

   • Yes
   • No
   • Not necessarily
   • Not known

10. Two quadrilaterals $$ABCD$$ and $$A_1B_1C_1D_1$$ satisfy$$AB = A_1B_1,\quad BC = B_1C_1,\quad CD = C_1D_1,\quad DA = D_1A_1.$$Are the quadrilaterals congruent?

    • Not necessarily
    • Definitely congruent
    • Definitely not
    • Not known