Deductive Geometry Challenge

證明平行四邊形的對邊是全等的。

• 由於隨機角度，平行四邊形的對邊不全等。

• 由於勾股定理，平行四邊形的對邊是全等的。

• 只有當平行四邊形是正方形時，對邊才是全等的。

• 由於平行四邊形的性質，對邊是全等的。

Using the Pythagorean theorem, find the length of the hypotenuse in a right triangle with legs of 3 and 4 units.

• 5

• 6

• 8

• 7

Show that the sum of the interior angles of a triangle is always 180 degrees.

• The sum of the interior angles of a triangle is always 180 degrees.

• The sum of the interior angles of a triangle is always 360 degrees.

• The sum of the interior angles of a triangle is always 270 degrees.

• The sum of the interior angles of a triangle is always 90 degrees.

Given two parallel lines cut by a transversal, prove that corresponding angles are congruent.

• Vertical angles are congruent when two parallel lines are cut by a transversal.

• Alternate interior angles are congruent when two parallel lines are cut by a transversal.

• Corresponding angles are supplementary when two parallel lines are cut by a transversal.

• Corresponding angles are congruent when two parallel lines are cut by a transversal.

Calculate the area of a rectangle with sides of length 5 units and 8 units.

• 56 square units

• 30 square units

• 13 square units

• 40 square units

Prove that the diagonals of a rhombus are perpendicular to each other.

• The diagonals of a rhombus intersect at a right angle.

• The diagonals of a rhombus are perpendicular to each other.

• The diagonals of a rhombus are parallel to each other.

• The diagonals of a rhombus are equal in length.

Solve for x: If two angles in a triangle measure 40 degrees and 70 degrees, what is the measure of the third angle?

• 70

• 90

• 40

• 110

Using the angle bisector theorem, find the length of a segment divided by an angle bisector.

• The length of the segment divided by an angle bisector is always equal to the length of the angle bisector

• The length of the segment divided by an angle bisector can be found by setting up a proportion: (Length of one segment)/(Length of other segment) = (Length of side opposite one angle)/(Length of side opposite the other angle)

• The angle bisector theorem only applies to right triangles

• The length of the segment divided by an angle bisector is calculated by adding the lengths of the two segments

Prove that the sum of the exterior angles of any polygon is always 360 degrees.

• The sum of the exterior angles of any polygon is always 270 degrees.

• The sum of the exterior angles of any polygon is always 180 degrees.

• The sum of the exterior angles of any polygon is always 450 degrees.

• The sum of the exterior angles of any polygon is always 360 degrees.

Calculate the volume of a cube with a side length of 6 units.

• 216 cubic units

• 216 square units

• 72 cubic units

• 36 cubic units