Prospect Hill Academy Heyl/Sparkes/Pfrommer Geometry Midterm Review Like all your midterms, your geometry midterm is worth 20% of your first semester grade. (10% of your year grade) Your midterm is broken into three sections as follows: Section 1 Short Answer ~25 questions 4 or 2 points each ~50% Section 2 Vocabulary/Notation ~20 questions 2 points each ~25% Section 3 Multiple Choice ~5 questions 2 points each ~5% Section 4 Free Response ~5 questions 4 points each ~20% Steps for studying: Organize materials- find old tests, quizzes, notes, portfolios. Review vocabulary—look up and make a list of any terms that you could not describe/identify/sketch. Look at skills list and identify places where you may be weak. Look through your notes, then work on some problems from those sections. Write down example problems and important theorems so you can look back at these later. Be awake, engaged, ask questions, answer questions, and be an active group/class member during in class reviews Work on problems from this review packet . Look back over old quizzes and portfolios, rework some of those problems. Night before- look over your written review materials, including the vocabulary list you created and the example problems you wrote. Sleep and eat breakfast!
Transcript
Prospect Hill Academy Heyl/Sparkes/PfrommerGeometry Midterm Review
Like all your midterms, your geometry midterm is worth 20% of your first semester grade. (10% of your year grade)
Your midterm is broken into three sections as follows:
Section 1 Short Answer ~25 questions 4 or 2 points each ~50%Section 2 Vocabulary/Notation ~20 questions 2 points each ~25%Section 3 Multiple Choice ~5 questions 2 points each ~5%Section 4 Free Response ~5 questions 4 points each ~20%
Steps for studying: Organize materials- find old tests, quizzes, notes, portfolios.
Review vocabulary—look up and make a list of any terms that you could not describe/identify/sketch.
Look at skills list and identify places where you may be weak. Look through your notes, then work on some problems from those sections. Write down example problems and important theorems so you can look back at these later.
Be awake, engaged, ask questions, answer questions, and be an active group/class member during in class reviews
Work on problems from this review packet .
Look back over old quizzes and portfolios, rework some of those problems.
Night before- look over your written review materials, including the vocabulary list you created and the example problems you wrote.
Sleep and eat breakfast!
Topics on Midterm ExamChapter 1
geometry vocabulary and notation draw and label a figure using correct notation given a written explanation using symbols Write a description of a geometric figure using correct notation and vocabulary.
Chapter 2: Reasoning in Geometry vertical angle conjecture, linear pair conjecture and properties of parallel lines and angles
find the slope of a line on a graph find the slope of a parallel or perpendicular line given the slope of a parallel or perpendicular
lineChapter 3: Triangle Properties
triangle sum conjecture- all the angles in a triangle add up to 180 Draw, label, and define the median and midsegment of a triangle. Solve problem using the definition of a midsegment, median, perpendicular bisector. Apply the Side-Angle Inequality Conjecture to determine the order of angles or sides from
least to greatest. isosceles triangle conjecture-base angles are congruent triangle inequality conjecture- Determine if any set of three given sides will make a possible
Chapter 5: Polygon Properties interior angle sum of a polygon, interior angles of regular polygons exterior angle sum of a polygon, exterior angles of regular polygons Given a description or a labeled picture, identify the most specific name of the figure (i.e.
square, rectangle, rhombus, and parallel). Given a shape, name what other quadrilateral categories it satisfies. Describe the relationship between squares/rectangles/rhombus/parallelograms Know all the properties/conjectures of trapezoids, kites, parallelograms, squares, rectangles,
rhombuses to solve problems for missing sides, angles, and sides and angles of the diagonals of the quadrilateral
Accurately label diagrams of kites, trapezoids, parallelograms with all their parts Find the length of a midsegment given the bases, or find a missing base given a midsegment
and one base of a triangle or trapezoidChapter 6: Circle Properties
Draw and identify the parts of a circle (chord, radius, tangent, diameter, minor arc, major arc, semicircle, secant, central angle)
Find missing arc lengths, chord lengths, and angle measurements using the chord properties and conjectures
Use the properties of tangents to solve for missing angles and lines in circle diagrams Apply the properties of inscribed/central angles to find missing angles and arc measures in a
given problem
Practice Problems-UNIT 11. Match each term with one of the items below.
II. Draw and label a diagram with the given information: 13. A line segment AB with midpoint M. 14. Draw ¿ BAK
15. Draw AB and EF so that AB ≅ EF 16. Draw DL and KF so that DL KF
17. Draw ¿ ABC that is 125º 18. Draw ¿ XYZ that is 20 º
19. Draw a plane that contains 4 points A, B, C, and D, with no more than 2 collinear points.
20. Draw an angle ¿ EFG. Now draw ray F⃗P as its angle bisector. Name and find the measure of all 3 angles.
III. Short Answer Questions: 21. What is the difference between a segment and a ray?
22. What point would be the vertex in ¿ BCS and how do you know ?
23. Draw a shape that is a polygon, and one that is NOT a polygon, and tell me why.Polygon Not a polygon
24. Draw a polygon that is convex, and one that is concave, and tell me why.Concave Convex
25. Draw a regular polygon, and explain why it is regular.
26. Draw and label an isosceles acute triangle CAT where AC ≅ CT
27. Draw circle J, with tangent lines AP and GW where AP ll GW.
28.What is a conjecture?
Use your definitions/vocab sheet to draw a picture for each of these examples, and then accurately LABEL all important information
A square LMNO A regular pentagon LABEL with diagonals LB and LE
Angle NAT= 110° with bisector A⃗S Parallelogram DOGS with DO ≅ GS
Line segment MR with a perpendicular bisector Right triangle GEO with B́A where MR = 19 ft G and E = 45°. Side GO = 30 ft
Circle with diameterSL, = 40 in Triangles ABC and DEF where and has tangents A⃗B and C⃗D where ABC ≅ DEF by SASA⃗B ll C⃗D
Two triangles CAT and DOG where Two triangles MAN and BOY whereCAT ≅ DOG by AAS MAN ≅ BOY by ASA
Unit 21. Determine the measure of each lettered angle.
2. Determine the measure of each lettered angle.
3. Triangle XYZ and two angle measures are shown in the diagram below. (multiple choice)
What is the measure of Y ?
A. 50°
B. 85°
C. 90°
D. 95°
4. The lines in the diagram below represent four streets in Linda's hometown. (multiple choice)
Keller Street is parallel to Garcia Street, and Main Street is parallel to Second Street.
If m 1 = 95°, what is m 2?
A. 75°
B. 85°
C. 95°
D. 105°
5. What is the slope of a line perpendicular to y = 3x + 6.7
6. What is the slope of a line parallel to y = 3x + 6.7
7. Find the slope of the line passing through (9, 5) and (-3, 1).
8. Line j is represented by the equation below.
line j: y = 2x + 4
a. What is the slope of line j? Show or explain how you got your answer.
b. What is the slope of any line that is parallel to line j? Explain your reasoning.
c. Write an equation for the line, k, that is parallel to line j and passes through the point with coordinates (3, 7). Show or explain how you got your answer.
d. Write an equation for the line, h, that is perpendicular to line j and passes through the point with coordinates (8, 10). Show or explain how you got your answer.
9. In the diagram below, .
Based on the angle measures in the diagram, what is the value of y?
A. 75
B. 90
C. 95
D. 120
10.The coordinate grid below shows point H(5, 2), point K(7, 10), and .
What is the slope of ? (Multiple Choice)
A.
B.
C.
D.
10. In the diagram below, intersects at point G.
Based on the angle measures in the diagram, what is the value of x?
A. 34
B. 38
C. 43
D. 56
11. Each of the two interior supports for part of a roof is perpendicular to a rafter, as shown below.
What is x, the measure, in degrees, of the angle formed by the two interior supports?
A. 50
B. 65
C. 90
D. 130
12. In the figure shown below, is parallel to , and intersects at Q.
What is the measure of ?
13. In the diagram below, lines k, m, and n are parallel lines intersected by line p.
Line p is not perpendicular to lines k, m, and n.
Which of the following angles has a measure that is not equal to the measure of 1 ? (multiple choice)
A. 2
B. 3
C. 4
D. 5
Unit 3
Use the information given to complete each statement. If the triangles are congruent, complete the statement and state the shortcut used. If the triangles are not congruent, state that they are not congruent.
a.
b.
c.
d.
2.
3. The diagram below shows
is an isosceles triangle with congruent sides and .
Point M lies on , and point N lies on . is parallel to . The length of is 23 feet, and the length of is 10 feet.
a. What is the length of ? Show or explain how you got your answer.
b. What is ? Show or explain how you got your answer.
c. What is ? Show or explain how you got your answer.
4.Are these triangles?? If not, draw or explain why it doesn’t work
19 cm, 33 cm, 48 cm 13 Km, 21 Km, 32 Km
37 n., 65 in., 92 in 17.1 ft, 21.4 ft, 34.8 ft
5.If you have a triangle with sides 24 and 41, what is the smallest possible third side, and what is the greatest possible third side?
The biggest possible side is ___________________________The smallest possible side is___________________________
6. Arrange these sides or angles from smallest to greatest:
7. III. Find the missing labeled angle or angles:
8. Solve for x and y
9. Solve for x
54
428412
ca
b
10
14
d
e
f
23
17
19
g
h
j
x68°
73°
125°51°
y
10.
12.Arrange the unknown letters from greatest to least.
13.
14.Arrange the unknown letters from greatest to least.
15.
16.Could you construct a triangle with lengths 23cm, 27cm and 50cm? Why or why not?
Diagram:G is the midpoint of NH and TU
Prove that NT ¿ HU
Statements Reasons
Given: Kite TARP with TA≅TPTR bisects<T
Prove: ¿ A≅<P
Reasons Statements
GT U
H
N
T
A
R
P
UNIT 41. Find all the lettered angles:
2. Find all the lettered angles:
3.
4. Find all the lettered angles
Section 2: A few short answer questions
81
76°
5. How many degrees are there in a 15 sided polygon? ____________
6. How do you find out how many degrees are in a polygon? (What is the formula)
7. The exterior angles of a polygon always add up to _____________.
8. If you have a regular hexagon, how many degrees is each of the interior angles?
9. If you have a regular decagon, each of the exterior angles is ________________.
10. If the measure of one exterior angle of a polygon is 15°, how many sides does the polygon have?
11. What is a kite? (Draw and label one)
12. What do you know about the non-vertex angles of a kite?
13. What do you know about the diagonals of a kite?
14. What is a trapezoid? (Draw and label one)
15. What do you know about the two angles on the left or right side of a trapezoid?
16. What is an isosceles trapezoid? (Draw and label one)
17. What do you know about each pair of base angles in an isosceles trapezoid?
18. What is a midsegment?
19. Draw a triangle with a midsegment drawn and labeled.
20. What do you know about the length of a midsegment of a triangle?
21. Draw a trapezoid with a midsegment drawn and labeled.
22. What do you know about the length of the midsegment of a trapezoid?
23. The following two problems are kites, find the missing angles or sides:
24. The following two problems are isosceles trapezoids, find the missing angles or sides:
25.
26.
27.
4)3)
29.30
33,
34.ABCD is a parallelogram
35. ABCD is a parallelogram
31.
32.
36.
37.
38.
UNIT 5
1. Find the perimeter
2. 3.
4. 5.
6. 7.
10.
12.Determine the measures of the arcs.
13.
14.
Review Problems
If you want some other problems to go back and try…
