Keating 2012 Geometry Midterm Review

1) ∠1 and ∠2 are vertical angles. If m∠1 is three times m∠2, find m∠1.

2) The measure of ÐCBG equals:

3) If two coplanar lines are parallel to the same line, then the lines are ______

4) Define parallel, perpendicular and skew lines. Use the diagram to give an example of each.

5) Name opposite rays with endpoint at A.

6) Write the converse of “If angle A is 90 degrees, then it is a right angle.”

7) If M is the midpoint of then what two segments are congruent?

8) If the measures of two supplementary angles are 3x – 2 and x – 68 , then the measure

of the larger angle is __?__.

9) If two angles are complementary to the same angle, then they are __?__ to each other

10) If m∠1 = and m∠2 =100, then the value of x is? What

type of angles are they?

11) In a plane, two lines perpendicular to the same line are __?__

12) Two lines parallel to the same plane are __?__

13) Identify the parts of an isosceles triangle PQR with the vertex at Q.

14) In LMN, if m∠L is 47 degree and m∠M = m∠N, then LMN is

15) For MNO and RST, if ∠N ∠S and ∠O ∠T, then the triangles are ?.

16) The measures of three interior angles of a quadrilateral are 72, 98 and 104, what is the

measure of the fourth angle?

17) The measure of each interior angle of a regular __?__ is 108.

18) The measure of each exterior angles of a regular convex dodecagon is __?__.

19) What type of regular polygon has 14 diagonals?

20) Find the measures of each interior angle of a regular polygon with 20 sides.

For questions 21-24, use the given diagram.

21) If QR ST, name the pairs of corresponding angles.

22) If QR ST, name the pairs of alt. interior angles.

23) If QR ST, name the same side interior angles.

24) If AB CD, then ∠1 must be __?__ to ∠8

25) What is the measure of angle NCD?

26) If l1 l2 and m∠5 = 33 and m∠2 = 74, what is m∠3?

27) Given JKL is isosceles with vertex K, find the

measure of ∠IJK.

28) If PQR DEF, name the 6 corresponding parts.

29) Given ABC XYZ, AB = 9, YZ = 14 and XY = , then the value of x is ?

30) Name the 5 ways to prove triangles congruent?

31) If CAT DOG, then name the 6 corresponding parts of the triangles.

32) What additional information is needed to show SRT UTR by the SSS Postulate?

33) Name the additional pair of corresponding parts that need to be congruent in order to

prove that FIG TOM by AAS.

34) Determine which triangles in the figure are congruent if ∠BAE ∠BCD and .

35) If XYZ is isosceles and , which angles are congruent?

36) Define and provide an example of a median, an altitude, and a perpendicular bisector?

37) List the properties of a parallelogram.

38) List the properties of a rectangle.

39) List the properties of a rhombus.

40) Which of the following methods can be used to prove a quadrilateral is a parallelogram?

I. Show that both pairs of opposite angles are congruent.

II. Show that the diagonals are perpendicular

III. Show that both pairs of opposite sides are congruent.

IV. Show that the diagonals bisect each other.

41) In parallelogram ABCD, if m∠A = 132, then m∠D =______.

42) If two polygons are similar then which of the following must be true?

I. The corresponding sides are in proportion

II. The perimeters are equal.

III. The corresponding sides are congruent.

IV. The corresponding angles are congruent.

43) What are the means and extremes of a proportion?

44) If , then identify the 4 properties of the proportion.

45) Name the 3 ways to prove two triangles are similar.

46) If ABC ~ DEF, which statements are true?

I. II. III. IV.

47) The angles in a hexagon have a ratio of 2:4:4:5:5:7. Find the measure of the angles.

48) The angles of a triangle are in the ratio 2:3:7. Find the measure of the angles.

49) What is scale factor?

50) Find the possible range for the third side of a triangle with sides of 2 and 18.

51) Find the possible range for the third side of a triangle with sides of 4x and 18x+3.

52) Is this triangle acute, right, or obtuse: 4, 5, and 6.

53) Is this triangle acute, right, or obtuse: 1, 1, and 9.

54) Is this triangle possible: 2, 3, and 10

55) Is this triangle possible: 4, 9, and 11

56) Use the Pythagorean theorem to find the missing side a right triangle:

a.  a = 12 and c = 13

b.  c = 10 and a = 4

c.  b = 18 and c = 20

57) Identify the parts and sides of a 30-60-90 and a 45-45-90 triangle.

58) Identify the definition of a parallelogram, the three properties of a parallelogram, and the four ways to prove that a quadrilateral is a parallelogram.

59) Define the midsegment of a triangle.

60) What are the formulas for the diagonals of a polygon, the interior angle sum of a polygon, the exterior angle sum of a polygon, each interior and each exterior angle of a polygon?

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