geometry main results - 10th Grade - Unit 6

Given l and m two parallel lines, and angle 2 = 47 degrees,

how much angle 5 would be?

• 47 degrees

• 43 degrees

• 133 degrees

• We don't know

Given l and m two parallel lines, what sentence is true?

• 1 = 2 = 3 = 4 and 5 = 6 = 7 = 8

• 1 = 6, 2 = 5, 4 = 7, 3 = 8

• 1 = 3, 3 = 6, 6 = 8, 2 = 4, 4 = 5, 5 = 7

• 1 = 7, 2 = 8, 4 = 6, 3 = 5

Given l parallel to m, and n parallel to p, which of the following are true? (choose all true)

• 1=3=5=7==9=11=13=15

• 4=10, 1=11, 8=2, 7=1, 16=10, 9=15

• 3 = 6 = 12 = 13, 1 = 10 = 15 = 8

• 2 = 12, 3 = 9, 6 = 4, 13 = 11

• 15 = 9, 7 = 2, 1 = 8, 10 = 15

Choose all sentences that are correct

• Two lines are parallels if and only if in any croosing lines, alternate internal angles are congruent

• Two lines are parallels if and only if in any croosing lines, alternate internal angles and same side internal angles are congruent

• Two lines are parallels if and only if in any croosing lines, corresponding angles are congruent

• Two lines are parallels if and only if in any croosing lines, alternate external angles are congruent

Given an isosceles triangle, find T

• 32 degrees

• 96

• 30 degrees

• 90 degrees

• neither

Choose all correct.

• Z is called circumcenter and it is the center of the only circumscribed circle on the triangle

• ZK = ZL = ZM

• Z is called INcenter and it is the center of the only circle inscribed in the triangle

• ZH = ZG = ZJ

• Given ZG = 65, and ZL = 16, we conclude that HJ = 126

QX and _ RX are angle bisectors of △PQR. And YX =19.2

Tell, which of the above sentences are true

• The distance from X to PQ is smaller than 19

• The angle PQR is of 104 degrees

• X is the circumscenter

• The incenter of the △PQR is X

• PQ could have more than one size

ABCD is a parallelogram.

Choose all correct sentences

• y = 11

• x is not an integer

• ∠A = 109°

• BC = 66.5

Use DESMOS to find the circumcenter and incenter, and the radii of the circumscribed and inscribed circles, respectively, to the triangle with vertices (5,0), (-1, -2) and (1,7)

Write the justification of each step and explain it.