Exploring Properties of Parallelograms and Trigonometry

The video tutorial covers a range of geometry topics, including properties of parallelograms, diagonals and angles in quadrilaterals, transformations and reflections, trigonometric ratios in right triangles, circle geometry with arcs and angles, and calculations of volume and surface area for different shapes. Key concepts such as supplementary and congruent angles, perpendicular diagonals, and the use of trigonometric ratios are explained in detail.

If the measure of angle CDA in a parallelogram is 64°, what is the measure of angle DAB?

• 116°

• 64°

• 180°

• 90°

In a parallelogram, if one angle measures 51°, what is the measure of the opposite angle?

• 90°

• 129°

• 180°

• 51°

In a rhombus, if one angle measures 90°, what is the measure of the other angles?

• 90°

• 45°

• 60°

• 30°

In a rhombus, if the measure of angle 1 is 90°, what is the measure of angle 3?

• 90°

• 71°

• 19°

• 109°

In a rectangle, if one diagonal measures 89.5 units, what is the measure of the other diagonal?

• 180 units

• 89.5 units

• 45 units

• 90 units

In a trapezoid, if AB is 74 units and DC is 182 units, what is the length of the mid-segment?

• 128 units

• 74 units

• 256 units

• 131 units

In a kite, if one diagonal measures 24 units, what is the measure of the angle bisected by this diagonal?

• 180°

• 66°

• 90°

• 24°

In a kite, if the measure of angle 2 is 90°, what is the measure of angle 3?

• 90°

• 180°

• 66°

• 24°

If a point is translated 4 units to the right and 10 units up, what is the new coordinate of the point (3, -3)?

• (-3, 12)

• (7, 7)

• (3, 7)

• (-1, 7)

Using the Pythagorean theorem, if one leg of a right triangle is 10 units and the hypotenuse is 15 units, what is the length of the other leg?

• 15 units

• 10 units

• 5 units

• 5√5 units