Download Geometry Test Theorems, Definitions, and Proofs Review Name

Geometry Test Theorems, Definitions, and Proofs Review
Name: _________________________________
Part One: Vocabulary
1. In an _________________________ we are given the hypothesis, and trying to prove the conclusion.
2. _________________________ is an argument that recognizes patterns in experiments or specific examples to draw
conclusions.
3. _________________________ is an argument that uses known facts in order to prove conclusions.
4. A line that crosses at least two other lines is called a ___________________________.
5. a) In the diagram to the right, angles 1 and 2 are a
__________________________________.
b) List a different pair of angles that also fit this description.
6. a) In the diagram to the right, angles 5 and 7 are
____________________________________.
b) List a different pair of angles that also fit this description.
7. a) In the diagram to the right, angles 2 and 6 are
____________________________________.
b) List a different pair of angles that also fit this description.
8. a) In the diagram to the right, angles 2 and 8 are
______________________________________.
b) List a different pair of angles that also fit this description.
9. a) In the diagram above, angles 4 and 6 are
____________________________________.
b) List a different pair of angles that also fit this
description.
10. a) In the diagram to the right, angles 3 and 6 are
___________________________________.
b) List a different pair of angles that also fit this description
11. a) In the diagram above, angles 1 and 8 are
______________________________________.
b) List a different pair of angles that also fit this
description.
12. Angles whose measures add together to give us 180 degrees are called _______________________.
13. Shapes are __________________ if corresponding angle measures are congruent and corresponding sides have
equal ratios.
14. Shapes are __________________ if corresponding angle measures are congruent and corresponding sides are
congruent.
15. The ratios of corresponding sides of similar figures are called the ____________________.
16. A line that cuts a line segment in half at a 90 degree angle is called a ________________________.
17. A line that cuts an angle in half is called an _____________________.
18. The line that connects the midpoint of a triangle’s side to its opposite vertex is called a _______________________.
19. Perpendicular bisectors of a triangle are _________________________.
20. The point where all three perpendicular bisectors of a triangle meet is called the ____________________ which is
the center of a _________________________ circle.
21. The point where all three angle bisectors of a triangle meet is called the __________________ which is the center of
an __________________________ circle.
22. The point where the medians of the triangle intersect is called the ____________________ which is the center of
gravity for the triangle.
23. A four sided figure is called a ____________________.
24. A quadrilateral that has exactly one pair of parallel sides must be a ________________________.
25. A parallelogram has opposite sides which are ____________________ and _____________________.
26. A ____________________ is a quadrilateral with two pairs of consecutive congruent sides.
27. A quadrilateral with four congruent sides and four right angles is called a ____________________.
28. A quadrilateral with four congruent sides and no right angles is called a ____________________.
27. A parallelogram with right angles and two different side measures in called a ________________________.
Part Two: For each of the following theorems or postulates fill in the blank, then draw and label a diagram
to represent the theorem.
28. Parallel Lines Postulate: Two lines cut by a transversal are parallel if
and only if ________________________ have equal measure.
Diagram:
29. Linear Pairs Postulate: If two angles are a linear pair, then the sum of
their measures is ____________.
Diagram:
30. Vertical Angle Theorem: If two angles are vertical angels, then their
measures are__________________.
Diagram:
31. Alternate Exterior Angle Theorem: Two lines cut by a transversal are
______________ if and only if alternate exterior angles are congruent.
Diagram:
32. ____________________________: Two lines cut by a transversal are
parallel if and only if same side exterior angles are supplementary.
Diagram:
33. Alternate Interior Angle Theorem: Two lines cut by a transversal are
parallel if and only if alternate interior angles are
______________________.
Diagram:
34. Same Side Interior Angle Theorem: Two lines cut by a transversal are
parallel if and only if same side interior angles are
_____________________________
Diagram:
35. ________________________ Theorem: the exterior angle of a
triangle has a measure equal to the sum of the measures of the two
remote interior angles.
Diagram:
36. Angle Addition Postulate: If P is a point in the interior of ∠𝐴𝐵𝐶, then
𝑚∠𝐴𝐵𝑃 + 𝑚∠𝑃𝐵𝐶 = _________________.
Diagram:
̅̅̅̅
37. _____________________________: If P is a point on segment 𝐴𝐵
then 𝐴𝑃 + 𝑃𝐵 = 𝐴𝐵.
Diagram:
38. Side-Angle-Side Similarity Theorem: If the angle of one triangle has
the same measure as an angle of a second triangle, and the lengths of
corresponding sides including these angles are multiplied by the same
scale factor then the two triangles are ___________________.
Diagram:
39. Angle-Angle Similarity Theorem: If the measure of two ________of
one triangle are the same as the measures of two _________of another
triangle then the two triangles are similar.
Diagram:
40. Side-Side-Side Similarity Theorem: If the lengths of the three side of
one triangle are multiplied by the same ______________ to obtain the
length of the three sides of another triangle , then the two triangles are
similar.
Diagram:
41. Hypotenuse-Leg Theorem: The hypotenuse leg theorem states that
any two _________ triangles that have a congruent hypotenuse and
a corresponding congruent leg are congruent triangles.
Diagram:
42. Midpoint Connector Theorem for Triangles: If a line segment joins the
midpoints of two sides of a triangle, then it is _______________to and
____________the length of the third side.
Diagram:
43. Triangle Proportionality Theorem: If a line parallel to one side of
a triangle intersects the other two sides of the triangle, then the line
divides these two sides _________________.
Diagram:
44. Midpoint Connector Theorem for Quadrilaterals: If the midpoints of
consecutive sides of any quadrilateral are connected, the resulting
quadrilateral is a________________.
Diagram:
45. Organize the following conditions into the section(s) they belong: SSS; SAS; SSA; ASA; AAS; AA; Hypotenuse-Leg
Similarity
Congruence
Not enough information to show
similarity or congruence
Part Three: Label each of the following diagrams using color to show every piece of information we know.
Ignore the place that says proof until you get to part four.
46. Given: AS bisects HAG; H  G
Proof:
B
47. Given: BF  ON ; BF || ON
O
R
Proof:
F
N
48. Given: AN  NL; LG  GE ; GNL  NGL; L is the midpoint of AE
N
Proof:
A
G
L
E
49. Given: GM  WH , MAAG , MA  HO , HOWO
Proof:
Part Four: For each of the diagrams above that you have labeled prove the following in the space provided
above.
̅̅̅̅ ≅ 𝐺𝑆
̅̅̅̅
For #46 prove 𝐻𝑆
For #47 prove R is the
midpoint of ̅̅̅̅
𝐵𝑁
For #48 prove ∠𝐴 ≅ ∠𝐸
For #49 prove ∆𝐺𝐴𝑀 ≅
∆𝑊𝑂𝐻