Geometry Paper Example: Four Coplanar Points

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George Washington University
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Name four coplanar points

Points G, D, F and A are coplanar (they lie in plane R )What is the intersection of plane P and plane R?

Line ADB.

Name a point that lies on both plane P and plane R

Point D

Name plane P and two more ways

Plane DEC

Plane BCE

To the nearest tenth, find the perimeter of ABC with vertices A (2, 4), B(-2,1) and C(2,1). Show your work.

d= 2(x2-x12+y2-y12) , where d is distance.

Distance between lines AB, BC and AC is given by :AB = 2(-2-22+1-42) = 5

BC = 2(2--22+1-12) = 4

AC = 2(2-22+1-42) = 3

Perimeter = 5 +4+3 = 12.0

Use the figure to complete each statement.

CD is the ___perpendicular bisector____of AB

If AB = 10, then EB = ___10__

AE = _of AB_____

__E__ is the midpoint of __AEB___

<BED = ___900___

If AB = 62, find the value of x. Show your work.

3x+16 2x-4

3x+16+2x-4=625x+12=625x5=62-125=505=10x=10Write a conditional statement. Write the converse, inverse and contrapositive for your statement and determine the truth value of each. If a statements truth value is false, give a counterexample.

Statement: If 6 <= x then 4 <= x: (TRUE)

Contrapositive: if 4!<= x then 6 !<= x where (!<=) means is not less or equal to.: (TRUE)

Converse: if 4 <= x then 6 < = x (FALSE) :If x is 5, 4 <= 5 but 6!<= 5

Inverse: if 6 !< = x then 4 !<= x : (FALSE)

If x = 5, 6 !<= 5 but 4 <= 5

Name two pairs of congruent angles and justify your answer.

Angle DAB and CAE are congruent (they are vertically opposite to each other)

Angle BAE and DAC are congruent (they are vertically opposite to each other.)

Write a two-column proof

Given: that the sum of angles in a column or row = 180 for lines DAE and BAC



Then DAB + BAE = CAE + BAE = 180 implies DAB = CAE and consequently BAE = DAC

Prove: x = 45

2x + 6 = 96

2x = 90

2x/2 = 90/2 = 45 , x = 45

Find the length of the third angle of a triangle given that the first two angles are 35 and 70. Show your work.

Angles in a triangle sum up to 1800Third angle = 180 35 -70 = 750Write a congruency statement for the pair of triangles

Triangle ABP = Triangle ABQ , since AQ = BP and AB is a shared line and angle BAQ is equal to angle ABP hence the triangles are equiangular and have same length in corresponding sides hence equal.

Find the values of x and y. Show your work.

4y + 8 = 24

4y = 24 -8 = 16 4y/4 = 16/4 = 4

Y = 4

7x -4 = 31

7x = 31 + 4 = 35

7x/7 = 35/7 = 5

X = 5 Which postulate or theorem, if any, could be used to prove the triangles congruent? If not enough information is given, write not enough information.

List the sides of each triangle from shortest to greatest

If AB is the midsegment, find the value of x. Show your work.

Find the coordinates of the circumcenter for DEF with coordinates D(1,1) E (7,1) and F(1,5). Show your work.

In triangle PQR, C is the centroid.

If CY = 10, find PC and PY

If QC = 10, find ZC and ZQ

If PX = 20, find PQ

For quadrilateral ABCD, determine the most precise name for it. A(2,3), B (12,3), C(8,6) and D(5,6). Show your work and explain.

For the parallelogram, find the value of the variables. Show your work.

5x + 2

3y 6 24


What is the length of the 2nd base of a trapezoid if the length of one base is 24 and the length of the midsegment is 19? Show your work.

What is the sum of the measures of the exterior angles in a heptagon? Explain.

Find the measure of each interior angle and each exterior angles of the following regular polygons. Show your work.







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