Geometry Final

in ABC the centroid D is on median AM. AD = x + 4 and DM = 2x - 4. Find AM

12

the sum of the interior angle measures of a polygon with s sides is 2340. find s

15

give an example of corresponding angles

angle 8 and angle 4

name the smallest angle of triangle ABC

angle B

triangle ABC has vertices A(0,10) B(4,10) and C(-2,4). find the orthocenter of triangle ABC

(-2, 12)

find the circumcenter of triangle EFG with E(4,4) F(4,2) and G(8,2)

(6, 3)

use the slope formula to determine the slope of the line containing points A(6,-7) B(9,-9)

-2/3

which three lengths could be the lengths of the sides of a triangle

10 cm 15 cm 24 cm

in quadrilateral ABCD, AE = X +6 and BE = 3x - 18. for what value of X is ABCD a rectangle

12

find the length of AB given that DB is a median of the triangle and AC = 26.

13

angle J and angle M are angles of an isosceles trapezoid JKLM. if angle J = 18X +8, and angle M = 11x + 15, find angle K

154

for the parallelogram if measurement of angle two = 4X -20 and the measurement of angle four = 3X -11 find the measurement of angle one

164

what is the measure of one interior angle in a regular 30 gon

168

DF bisects EDG. find the value of X.

19

find the measurement of angle K

The measurement of angle K = 63°

identify the transversal and classify the angle pair 11 and angle seven

The transversal line is L. the angles are corresponding angles.

find angle E and angle N, given angle F = angle P, E = (x^2)°, and N = (4x^2 - 75)°

angle E = 25° angle N = 25°

find the measurement of angle Q

angle Q = 75°

measurement of angle a equals 9X -7, measurement of angle B = 7x - 9, and measurement of angle C equals 28 - 2X. list the sides of triangle ABC in order from shortest to longest.

AB; AC; BC

DEFG is a rectangle. DF = 5X -3 and EG = X +5. find the value of X and the length of each diagonal

...

for these triangles select the triangle congruence statement and the postulate or theorem that supports it.

ABC = JKL; HL

ABC is an isosceles triangle. AB is 4X +4. BC = 8X +3 and CA = 7X +8. Find AB

AB equals 24

identify a pair of parallel segments

AB is parallel to EH

determine if the conditional statement is true. if a figure has four sides, then it is a square

false; a rectangle has four sides, and it is not a square

two sides of a triangle have lengths 6 and 17. which expression describes the length of the third side

greater than 11 and less than 23

identify the hypothesis and conclusion of the conditional statement

hypothesis: it is raining conclusion: it is cloudy

write a conditional statement from the statement a horse has four legs

if it is a horse, then it has four legs

which description does not guarantee that a quadrilateral is a square?

is a parallelogram with perpendicular diagonals

two sides of a triangle have lengths 10 and 15. what must be true about the length of the third side

less than 25

find the measure of angle ABC

measurement of angle ABC = 35°

on the measure of each numbered angle

measurement of angle one = 54°, measurement of angle 2 = 63°, measurement of angle 3 = 63°

find the measurement of angle one in the diagram

measurement of angle one equals 135°

find the measurement of angle one in the diagram

measurement of angle one equals 95°

use the slopes to determine whether the lines are parallel perpendicular or neither. AB and CD for A(3,5) , B(-2,7) , C(10,5) , and D (6,15)

neither

name the point of concurrency of the angle bisectors

not shown

classify triangle DBC by it's angle measures, given DAB = 60°, ABD = 75°, and BDC = 25°

obtuse triangle

which venn diagram is not correct

rectangles inside squares

The figure shows part of the roof structure of a house. use SAS to explain why RTS = RTU.

[1] ST = UT [2] RTS = RTU [3] RT = RT

solve the equation 4X -6 = 34

[1] addition property of equality [2] division property of equality

write a justification for each step

[1] angle addition postulate [2] division property of equality

show ABD equals CDB for A = 3

[1] A +7 [2] 4a -2 [3] 16 [4] 16 [5] SAS

The measurement of angle R = 120 and the measurement of angle S = 110. Find the measurement of angle T.

20

which three lengths cannot be the lengths of sides of a triangle?

21 m, 6m, 10 m

points B, D, and F are midpoints of the sides of ACE. EC = 30 and DF = 17. Find AC

34

LM is the midsegment of parallelogram ABCD. AB = X +8 LM = 4x + 3 DC = 243 what is the value of X

35

in a swimming pool two lanes are presented by lines L and M. if a string of flags strung across the lanes is represented by transversal T, and x=10, show that the lanes are parallel

3X +4 = 3×10+4 = 34°; 4X -6 = 4×10-6 = 34° The angles are alternate interior angles and they are congruent, so the lanes are parallel by the converse of the alternate interior angles theorem

Q is equidistant from the sides of TSR. find RST

42

find the length of the midsegment. the diagram is not to scale

42

one of the acute angles in a right triangle has a measure of 34.6°. what is the measure of the other acute angle?

55.4°

what is the sum of the interior angle measures of a 35 gon

5940

in the parallelogram the measurement of angle QRP = 32 and the measurement of angle PRS = 84. find PQR.

64

two sides of a triangle have lengths 5 and 12. which inequalities represent the possible lengths for the third side, x?

7 < x < 17

use the information in the diagram to determine the height of the tree

75 feet

find the value of X

8

ABF is congruent to EDG. ABF and GCS are equilateral. AG equals 21 and CG equals 1/4 AB. find the total distance from A to B to C to D to E.

98

which diagram shows a point P an equal distance from point A B and C?

A

given: ABC is congruent to MNO identify all pairs of congruent corresponding parts

A = M, B = N, C = O, AB = MN, BC = NO, AC = MO

A pilot uses triangles to find the angle of elevation A from the ground to her plane. how can she find the measurement of angle A?

ABO = CDO by SAS and angle A = angle C by CPCTC, so the measurement of angle A = 40° by substitution.

given the length Mark on the figure and AD bisects BE, use SSS to explain why ABC equals DEC.

AC = CD, AB = ED, BC = CE

given that ABC = DEC and E = 23°, find ACB

ACB = 67°

name a median for triangle ABC

BD

in ACE, G is the centroid and BE = 16. Find BG and GE.

BG = 6, GE = 12

find CA

CA = 14

for the conditional statement write the converse and a biconditional statement: a figure is a square if and only if it is a rectangle

Converse if a squared plus B squared equals C squared than the figure is a right triangle with sides A B & C biconditional: a figure is a right triangle with sides A B and C if and only if A squared plus B squared equals C squared

find DCB, given A = F, B = E and and CDE = 46°

DCB = 46°

which statement is not necessarily true? given: DE is the perpendicular bisector of JL

DK = KE

Daphne folded a triangular sheet of paper into the shape shown. find ECD, given CAB = 61°, ABC = 22° , and BCD = 42°

ECD = 41°

List the sides in order from shortest to longest

LK; LJ; JK

write a two column proof. given: T is perpendicular to L, angle one is congruent to angle 2 prove: M is parallel to L

T is perpendicular to L, angle one is congruent to angle two

determine if the biconditional is true. if false give a counterexample: a figure is square if and only if it is a rectangle

The biconditional is false. A rectangle does not necessarily have four congruent sides

to Seyfert galaxies, BW tauri and M77, represented by points A and B, are equidistant from Earth, represented by point C. What is the measurement of angle A?

The measurement of angle A = 65°

The rhombus the measurement of angle one = 140. what are the measurements of angle two and angle three?

The measurement of angle two = 140, the measurement of angle three = 20

in the rhombus the measurement of angle one = 15x, the measurement of angle two = X + Y, and the measurement of angle three equals 30Z. find the value of each variable

X = 6, Y = 84, Z = 3

find the missing values of the variables.

X = 93, Y = 74

find the value of X

X = six

write and solve inequality for X

X is greater than two

two sides of an equilateral triangle measure (2y + 3) units and (y^2 - 5) units. if the perimeter of the triangle is 33 units what is the value of Y?

Y = 4

given RT is perpendicular to SU, SRT is congruent to URT, RS = RU, T is the midpoint of SU

[1] definition of perpendicular lines [2] third angles theorem [3] reflexive property of congruence

use the given plan to write a two column proof: given: measurement of angle one + measurement of angle two = 90°, measurement of angle 3+ measurement of angle four = 90°, measurement of angle two = measurement of angle three

[1] measurement of angle 3+ measurement of angle four = 90° [2] substitution property [3] subtraction property of equality

fill in the blanks to complete the two column proof. given: angle one and angle two are supplementary the measurement of angle 1 = 135°

[1] measurement of angle one equals 135° [2] definition of supplementary angles [3] subtraction property of equality

write a justification for each step given that EG = FH

[1] segment addition postulate [2] substitution property of equality

Given: angle 1+2 = 180° prove: L is parallel to M

[1] vertical angle theorem [2] converse of the same side interior angles theorem

Tom is wearing his favorite bowtie to the school dance. The bowtie is in the shape of two triangles. given: AB = ED, BC = DC, AC = EC, A = E prove: ABC = EDC

[1] vertical angles theorem [2] third angles theorem [3] ABC = EDC

what is the name of the segment inside the large triangle

altitude

write the definition as a bike biconditional: an acute angle is an angle whose measure is less than 90°

an angle is acute if and only if it's measures less than 90°

find angle one angle three in the kite

angle one = 17 angle three = 73

find the measure of the numbered angles in the rhombus

angle one = 90, angle two = 24, angle three = 66

what type of angle pair is Angle one angle four

angle one angle four are corresponding angles

use the converse of the corresponding angles postulate and angle one is congruent to angle two to show that L is parallel to M

angle one is congruent angle two is given. from the diagram angle one and angle two are corresponding angles. so by the converse of the corresponding angles postulate L is parallel to M

use the information measurement of angle 1 is (3x + 30)° and measurement of angle 2 = (5x-10)°, and x = 20, and the theorems you have learned to show that L is parallel to M.

by substitution angle one equals 3×20+30 = 90° and angle two equals 5×20-10 = 90°. by the substitution property of equality angle one equals angle two equals 90°. by the converse of the alternate interior angles theorem, L is parallel M.

three security cameras were mounted at the corners of a triangular parking lot. camera one was 156 feet from camera two which was 101 feet from Camera three. cameras one and three were 130 feet apart. which camera had to cover the greatest angle?

camera three

write the conditional statement and converse within the biconditional: a rectangle is a square if and only if all four sides of the rectangle are equal length

conditional: if all four sides of the rectangle are equal length then it is a square Converse: if a rectangle is a square then it's four sides are equal length

write the converse, inverse, and contrapositive: if an animal is a bird, then it has two eyes

converse: if an animal has two eyes then it is a bird inverse: if an animal is not a bird then it does not have two eyes contrapositive: if an animal does not have two eyes then it is not a bird

classify triangle ABC by its side lengths

equilateral triangle

A jeweler creates triangular medallions by bending pieces of silver wire. each medallion is an equilateral triangle. each side of a triangle is 3 cm long. how many medallions can be made from a piece of wire that is 65 cm long?

seven medallions

from the ocean salmon swim perpendicularly toward the shore to lay their eggs in rivers. waves in the ocean are parallel to the shore. why must the salmon swim perpendicularly to the waves?

swimming salmon form a transversal to the shore and the waves. The shore and the waves are parallel, and the swimming salmon are perpendicular to the shore, so by the perpendicular transversal theorem, the salmon are perpendicular to the waves.

how many true conditional statements may be written using the following statements: n is a rational number. n is an integer n is a whole number

three conditional statements

identify the property that justifies the statement: AB is congruent to CD and CD is congruent to EF so AB is congruent to EF

transitive property of congruence

find the value of X

x = 45

determine if you can use HL congruence theorem to prove ACD = DBA. if not tell what else you need to know.

yes