Midterm Review

1.2 – Points, Lines and Planes

• Name the plane at the front of the prism.• Name the intersection of the front plane and

bottom plane• Name 2 collinear points• Name 3 coplanar point

1.3 – Segment Addition

• BC = 3x + 2 and CD = 5x − 10. Solve for x.

1.3 – Segment Addition

• Points A, B, and C are collinear with B between A and C. AB = 4x − 1, BC = 2x + 1, and AC = 8x − 4. Find AB, BC, and AC.

1.4 – Angle Addition

• In the figure at the right, mPQR = 4x + 47. Find mPQS.

1.5 – Angle Pair Relationships

• Name an angle described by each of the following– supplementary to NQK– vertical to PQM– congruent to NQJ

1.5 – Angle Pair Relationships

• XYZ and XYW are complementary angles. mXYZ = 3x + 9 and mXYW = 5x + 9. What are mXYZ and mXYW ?

1.5 – Angle Pair Relationships

• SQ bisects RST. mQST = 2x + 18 and mRST = 6x − 2. What is mRSQ?

1.7 – Distance and Midpoint

• Find the distance and midpoint for the followingQ(−7, −4), T(6, 10)

1.7 – Distance and Midpoint

• A map of a city and suburbs shows an airport located at A(25, 11). An ambulance is on a straight expressway headed from the airport to Grant Hospital at G(1, 1). The ambulance gets a flat tire at the midpoint M of . As a result, the ambulance crew calls for helicopter assistance.– a. What are the coordinates of point M?– b. How far does the helicopter have to fly to get from M to

G? Assume all coordinates are in miles.

1.8 – Polygons and Area

• Find the perimeter and area for the figure

1.8 – Polygons and Area

• Find the perimeter and Area for the figure

2.1 – Inductive Resoning

• Find the next term in the sequence1, 4, 9, 16, 25, . . .

• Find a counterexample for the followingA four-sided figure with four right angles is a square.

2.2 & 2.3 - Conditionals

• Write the following as a conditional. Then write the converse, inverse, and contrapositive. Determine the Truth values. If the converse and conditional are true, create a biconditional

2.4 – LOD and LOS

• Can you determine a conclusion from the following. If so which law?

If Shauna is early for her meeting, she will gain a promotion. If Shauna wakes up early, she will be early for her meeting. Shauna wakes up early.

2.5 - Proofs

• Name the properties that justify each step3x = 24; x = 8x = y; If x = 18, then y = 18AB = CD, CD = EF. Therefore, AB = EF.A A

2.6 – Angle Pair Relationships

• Solve for the variable

3.1 – Parallel Lines

• Name a pair of parallel lines• Name a pair of parallel planes• Name a pair of skew lines

3.1 – Parallel Lines

• Name a pair of the following– Corresponding Angles– Alternate Interior Angles– Alternate Exterior Angles– Same Side Interior Angles

3.2 – Parallel Lines

• Find the measure of the numbered angles. Justify your answer

3.3 – Parallel Lines

• Solve for the variables

3.5 – Triangle Angles

• Solve for the variables

3.7 – Slope

• Find the line in slope intercept form that intersects both pointsA(4, 2), B(6, −3)

3.8 – Parallel and Perpendicular Slope

• Find the equation of the line that is parallel to the given line that intersects the given point.y = x − 7, (0, 4)

3.8 – Parallel and Perpendicular Slope

• Find the equation of the line that is parallel to the given line that intersects the given point.y = −2x, (4, 0)

4.1 - Triangles

• The triangles are congruent• Write congruence statements for ALL

congruent parts for the following triangles.

4.2 – 4.4 – Triangle Congruency

• Can you prove these triangles congruent. Justify your answer

4.5 – Isosceles and Equilateral Triangles

• Solve for the variables

4.6 – Overlapping Triangles

• Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.

5.1 – Midsegment in Triangle

• Solve for the variable

5.1 – Midsegment in Triangle

• A sinkhole caused the sudden collapse of a large section of highway. Highway safety investigators paced out the triangle shown in the figure to help them estimate the distance across the sinkhole. What is the distance across the sinkhole?

5.2 – Angle and Perpendicular Bisectors

• Solve for the variables

5.2 – Angle and Perpendicular Bisectors

• Find an equation in slope-intercept form for the perpendicular bisector of the segment with endpoints H(–3, 2) and K(7, –5).

5.3 - Perpendicular and Angle Bisectors

• Find the center of the circle that you can circumscribe about ABC.

• A (2,8)• B (0,8)• C (2,2)

5.4 – Medians

• In DEF, L is the centroid.– If HL = 30, find LF and HF.– If KE = 15, find KL and LE.– If DL = 24, find LJ and DJ.

5.4 - Altitudes

• Find the orthocenter of the following triangle• A (2,8)• B (0,8)• C (2,2)

5.6 – Triangle Inequality

• Can a triangle have the following side lengths• 8 ft, 9 ft, 18 ft

5.6 – Triangle Inequality

• List the sides of each triangle in order from shortest to longest.

5.6 – Triangle Inequality

• Two sides of a triangle have side lengths 8 units and 17 units. Describe the lengths x that are possible for the third side.

5.7 – Triangle Inequality

• Find the range for the variable

6.1 – Polygon Angle Sum Theorem

• Solve for the variable

6.1 Polygon Angle Sum Theorem

• Find the measure of one interior angle and the measure of one exterior angle in each regular polygon.

• 20-gon

6.2 & 6.3 - Parallelograms

• Find the values of the variables in the parallelogram

6.4 & 6.5 – Special Parallelograms

• Solve for the numbered angles

6.4 & 6.5 – Special Parallelograms

• Solve for the variable in this rhombus

6.6 – Kites and Trapezoids

• Solve for the numbered angles

6.6 – Kites and Trapezoids

• Solve for the variable

6.7 – Polygons in Coordinate Plane

• Classify the following polygonA(3, 5), B(6, 5), C(2, 1), D(1, 3)

6.8 – Polygons in Coordinate Plane

• Give coordinates for points D and S without using any new variables.

RHOMBUS TRAPEZOID

7.1 – Ratios and Proportions

• Solve for the variable

12 4

2 5x x

7.1 – Ratios and Proportions

• The measures of two complementary angles are in the ratio 7 : 11. What is the measure of the smaller angle?

7.2 – Similar Figures

• These figures are similar. Solve for the variables

7.3 – Similar Triangles

• Can you prove that the triangles are similar? If so, write a similarity statement and tell whether you would use AA , SAS , or SSS .

7.4 – Geometric Mean

• Find the geo mean for the following5 and 80

7.4 – Geometric Mean

• Solve for the variables

7.5 – Side Splitter and Triangle Angle Bisector

• Solve for x