Theorem

Question 1

Opposite sides of a parallelogram are congruent.

Answer 1

Theorem 1

Question 2

A diagonal of a parallelogram forms two
congruent triangles.

Answer 2

Theorem 2

Question 3

Opposite angles of a parallelogram are congruent.

Answer 3

Theorem 3

Question 4

Consecutive angles of a parallelogram are supplementary.

Answer 4

Theorem 4

Question 5

The diagonals of a parallelogram bisect each other.

Answer 5

Theorem 5

Question 6

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Answer 6

Theorem 6

Question 7

If one pair of opposite sides of a
quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

Answer 7

Theorem 7

Question 8

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Answer 8

Theorem 8

Question 9

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is parallelogram.

Answer 9

Theorem 9

Question 10

The diagonals of a rectangle are congruent.

Answer 10

Theorem 10

Question 11

The diagonals of a rhombus are perpendicular.

Answer 11

Theorem 11

Question 12

Each diagonal of a rhombus bisects two angles of the rhombus.

Answer 12

Theorem 12

Question 13

Base angles of an isosceles trapezoid are congruent.

Answer 13

Theorem 13

Question 14

If the base angles of a trapezoid are congruent, then the trapezoid is isosceles.

Answer 14

Theorem 14

Question 15

The diagonals of an isosceles trapezoid are congruent.

Answer 15

Theorem 15

Question 16

If the diagonals of a trapezoid are congruent then, the trapezoid is isosceles.

Answer 16

Theorem 16

Question 17

The diagonals of a kite are perpendicular.

Answer 17

Theorem 17

Question 18

In a kite, one diagonal bisects the other diagonal.

Answer 18

Theorem 18

Question 19

In a kite, one of the diagonals bisects the angles at its endpoints and the other two angles are congruent.

Answer 19

Theorem 19

Question 20

The segment that joins the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side.

Answer 20

Theorem 20
The Midline/Midsegment Theorem

Question 21

If three or more parallel lines cut off congruent segments on one transversal, then the parallel lines cut off congruent segments on any transversal cutting the parallel lines.

Answer 21

Theorem 21

Question 22

The median of a trapezoid is parallel to the bases and has a length equal to half the sum of the lengths of the bases.

Answer 22

Theorem 22
Median of a Trapezoid Theorem

Question 23

If a line is drawn from the midpoint of one side of a triangle and parallel to a second side, then it passes through the midpoint of the third side.

Answer 23

Theorem 23

Question 24

If two polygons are similar, then the ratio of
their perimeters is equal to the ratio of any two
corresponding sides.

Answer 24

Theorem 24

Question 25

Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.

Answer 25

Theorem 27

Question 26

Converse of the Triangle Proportionality Theorem If a line divides the two sides of a triangle proportionally, then the line is parallel to the third side.

Answer 26

Theorem 28

Question 27

Proportional Segments Theorem If three parallel lines have two transversals, then they divide the transversals proportionally.

Answer 27

Theorem 29

Question 28

Triangle Angle-Bisector Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.

Answer 28

Theorem 30

Question 29

Right Triangle Similarity Theorem The altitude to the hypotenuse of a right triangle forms two triangles that are similar to the original triangle and similar to each other.

Answer 29

Theorem 31

Question 30

Geometric Mean Theorem 1 The length of the altitude drawn to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse. If ABC is a right triangle with mC = 90, and 𝐶𝑃 ⊥ 𝐴𝐵, then 𝑪𝑷 = 𝑩𝑷 ∙ 𝑨𝑷.

Answer 30

Theorem 32

Question 31

Geometric Mean Theorem 2 The altitude to the hypotenuse of a right triangle intersects the hypotenuse such that the length of each leg is the geometric mean between the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuse.

Answer 31

Theorem 33

Question 32

Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the square of the lengths of the legs.

Answer 32

Theorem 34

Question 33

Converse of the Pythagorean Theorem If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

Answer 33

Theorem 35

Question 34

If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is an obtuse triangle.

Answer 34

Theorem 36

Question 35

If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle.

Answer 35

Theorem 37

Question 36

The 45 - 45 - 90 Theorem In a 45 - 45 - 90 triangle, the length of the hypotenuse is 2 times the length of a leg.

Answer 36

Theorem 38

Question 37

The 30 - 60 - 90 Theorem In a 30 - 60 - 90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3 times the length of the shorter leg.

Answer 37

Theorem 39