Name _____________________________________________ Date _________ Test Review (2.1 to 2.12) CC Geometry

1. The triangles ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹 in the figure below are such that 𝐴𝐵̅̅ ̅̅ ≅ 𝐷𝐸̅̅ ̅̅ , 𝐴𝐶̅̅ ̅̅ ≅ 𝐷𝐹̅̅ ̅̅ , and ∠𝐴 ≅ ∠𝐷. Which criteria for triangle congruence implies that ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹?

2. Given: JI KOHO

Prove: KJHHIK

3. Given: CGDG , FCAD , EDBC

Prove: EB

Statements Reasons

Statements Reasons

Reflexive Property In a triangle, angles opposite congruent sides are congruent

In a triangle, angles opposite congruent sides are congruent

Reflexive Property

Addition Property

Corresponding parts of congruent triangles are congruent

4. Given: AEC is an isosceles triangle with AEAC , AFAB , FDEBDC

Prove: FDECDB

5. Given: DC , AB bisects < 𝐶𝐴𝐷

Prove: a) DABCAB b) DBCB c) AB bisects CD

Statements Reasons

Statements Reasons

In a triangle, angles opposite congruent sides are congruent Subtraction Property

A bisector divides an angle into two congruent parts Reflexive Property

Corresponding parts of congruent triangles are congruent Since CD was divided into two congruent parts, then CD was bisected

6. Given: BCFA , FCFE , DCFC , DCFE

Prove: a) ADCBFE

7. Given the following parallelogram, find the value of x and y.

8. If UZ = x + 21 and ZS = 3x – 15, find US.

A C B

D E

F

G

Statements Reasons

R

U

S

T

Z

Reflexive Property Addition Property

Perpendicular lines form right angles

All right angles are congruent

9. Given parallelogram ABCD with AC = 34, AB = 26, and BD = 28, find the perimeter of △ 𝐶𝐸𝐷. Justify your solution

10. Find the measure of the numbered angles in each rhombus: a) b)

11. The diagram below is of rectangle ABCD. Diagonals BD and AC intersect at E. a) If AE = 4x+10 and EC = 2x +32, find x.

b) If AC = 6w -18 and BD = 3w+3, find the length of BD.

1

4

104o 2

3

12. Given: Parallelogram ABCD, FCAE Prove: (a) CFBAED (b) DFBE is a parallelogram

13. Given: Rectangle ABCD, CEDF Prove: (a) BCFADE (b) 21 (c) GFE is isosceles

Statements Reasons

Statements Reasons

Reflexive Property Addition Property In a rectangle, opposite sides are congruent

In a rectangle, all angles are right angles

All right angles are congruent

Corresponding parts of congruent triangles are congruent A triangle with two congruent sides is isosceles

In a parallelogram, opposite sides are congruent In a parallelogram, opposite angles are congruent

Subtraction Property

Since both pairs of opposite sides are congruent, DFBE is a parallelogram

Corresponding parts of congruent triangles are congruent

14. Given: Parallelogram ABCD

CEAF

ACBF

ACDE

Prove: BFCDEA

15. Given: Parallelogram DEBK, DABC , BLDJ Prove: ALCJ

Statements Reasons

Statements Reasons

Perpendicular lines form right angles

All right angles are congruent

Reflexive Property

Subtraction Property In a parallelogram, opposite sides are congruent

A triangle with a right angle is a right triangle

Reflexive Property

Addition Property

In a parallelogram, opposite sides are parallel If parallel lines are cut by a transversal alternate interior angles are congruent

Corresponding parts of congruent triangles are congruent

A) The opposite angles of a parallelogramare congruent.

B) The opposite sides of a parallelogram arecongruent.

C) The diagonals of a parallelogram bisecteach other.

D) The diagonals of all parallelograms areperpendicular to each other.

16. Which of the following statements is false?

17. As shown in the diagram below, the diagonalsof parallelogram QRST intersect at E. If

, , and ,determine TE algebraically.

A)B)C)D)

18. In the diagram below, parallelogram ABCD has diagonals and that intersect atpoint E.

Which expression is not always true?

A) 15° B) 30° C) 45° D) 60°

19. In the diagram below of parallelogram ABCD with diagonals and , m 1 = 45 and m

DCB = 120.

What is the measure of 2?

A) –30 B) 30 C) –6 D) 6

20. In the accompanying diagram of parallelogramABCD, diagonals and intersect at E,

, and .

What is the value of x?

D

A) B) C) bisects DAB and BCD.D) and bisect each other.

21. If quadrilateral ABCD is a parallelogram,which statement must be true?

22. In the accompanying diagram of parallelogramABCD, m A = x + 17 and m C = 2x - 4. Findthe value of x.

23. In parallelogram ABCD, m A = 4x – 17 andm C = 2x – 5. Find the value of x.

A) I and II B) I and IIIC) II and III D) I, II, and III

24. Which set of statements would describe aparallelogram that can always be classified asa rhombus?

I. Diagonals are perpendicular bisectors ofeach other. II. Diagonals bisect the angles from whichthey are drawn. III. All four sides are congruent.

25. In the accompanying diagram of rhombus ABCD, m CAB = 35. Find m CDA.

26. In the accompanying diagram of rhombus ABCD, the lengths of sides and arerepresented by 3x - 8 and 2x + 1, respectively.Find the value of x.

A) 15 B) 18 C) 24 D) 30

27. In the diagram below of rhombus ABCD, thediagonals and intersect at E.

If AC = 18 and BD = 24, what is the length ofone side of rhombus ABCD?

A) All squares are parallelograms.B) All squares are rectangles.C) All rectangles are squares.D) All rectangles are parallelograms.

28. Which of the following statements is false?

29. In rectangle ABCD, diagonal AC = x + 10 anddiagonal BD = 2x - 30. Find the value of x.

A) are congruentB) bisect each otherC) bisect the angles through which they passD) are perpendicular to each other

30. A parallelogram must be a rectangle if itsdiagonals

A) II and III, only B) I and II, onlyC) I and III, only D) I, II, and III

31. Which statements describe properties of thediagonals of a rectangle?I The diagonals are congruent.II The diagonals are perpendicular.III The diagonals bisect each other.

A) B)C) D)

32. In the accompanying diagram, ABCD is asquare with diagonal . Which statement isnot true?

A) rhombus B) squareC) rectangle D) parallelogram

33. Which quadrilateral must have diagonals thatare congruent and perpendicular?

A) Rhombuses are squares.B) Parallelograms are rectangles.C) Rectangles are squares.D) Squares are rectangles.

34. Which statement is always true?

A) rectangle B) rhombusC) square

35. Which quadrilateral does not always havecongruent diagonals?