Chapter 6 Geometry Practice

Find the coordinates of the circumcenter of the triangle with the given vertices: T(-6,-5), U(0,-1), V(0,-5)

(-3,-3)

Find the coordinates of the centroid of the triangle with the given vertices: A(-10,3), B(-4,5), C(-4,1)

(-6,3)

Find the coordinates of the vertices of the midsegment triangle for the triangle with the given vertices: A(-6,8), B(-6,4), C(0,4)

(-6,6), (-3,6), (-3,4)

Find the coordinates of the vertices of the midsegment triangle for the triangle with the given vertices: D(-3,1), E(3,5), F(1,-5)

(0,3), (2,0), (-1,-2)

Find the coordinates of the centroid of the triangle with the given vertices: D(2,-8), E(2,-2), F(8,-2)

(4,-4)

Find the coordinates of the circumcenter of the triangle with the given vertices: X(-2,1), Y(2,-3), Z(6,-3)

(4,3)

Find the circumcenter of triangle ABC with vertices A(12,0), B(0,-6), and C(0,0)

(6,-3)

Your friend is trying to balance a triangle on the tip of his pencil. Find the coordinates on the centroid if the triangle as vertices of (2,4), (10,6), and (12,-10)

(8,0)

Write and solve an inequality for the possible values of x (slide 13)

0 ﹤x ﹤8

Write and solve an inequality for the possible values of x (slide 12)

1/3 ﹤ x ﹤ 12

Find the measure of PQ (slide 1)

10.2

Find the measure of DC (slide 16)

20

Find the measure of RS (slide 17)

23

Describe the possible lengths of the third side of the triangle given the lengths of the other two sides: 6 meters, 9 meters

3 m ﹤x ﹤15m

Write and solve an inequality for the possible values of x (slide 14)

3 ﹤x﹤7

Given m∠B = 66°, m∠BAD = 34°, and AD bisects ∠BAC, find m∠DAC (slide 3)

34°

Describe the possible lengths of the third side of the triangle given the lengths of the other two sides: 4 inches, 8 inches

4 in ﹤x ﹤12in

Find the measure of JM (slide 2)

46

Find the measure of ∠JFH (slide 18)

47

Find the length of SR (slide 7)

6

Find the length of TS (slide 8)

6

Describe the possible lengths of the third side of the triangle given the lengths of the other two sides: 11 feet, 18 feet

7 ft ﹤x ﹤29ft

Find the length of CD (slide 6)

8

Given m∠B = 57°, m∠C = 51°, and AD bisects ∠BAC, find m∠ADC (slide 3)

93°

Compare AC to XZ (slide 11)

AC ﹤XZ

Write an indirect proof of the statement "In triangle XYZ, if XY = 4 and XZ = 8, then YZ is greater than 4."

Assume temp that YZ is not greater than 4. Then, it follows that either YZ ﹤4 or YZ = 4. If YZ ﹤4, then XY+YZ﹤XZ bc 4+4=8. Both conclusions contradict the Triangle Inequality Theorem which says that XY + YZ is greater then XZ. So, the temp assumption that YZ is not greater then 4 cannot be true. This proves that in trianlge XYZ, if XY = 4 and XZ = 8, then YZ is greater than 4

Use the diagram on slide 20: If RQ = RS and m∠QRT is greater than m ∠SRT, then how does QT compare to ST?

QT is greater than ST

In triangle PQR, SP = 78, and UM = 19. Find SM, MR, and UR. (slide 5)

SM = 26 MR = 38 UR = 57

Compare TU to SV (slide 9)

TU ﹥ SV

Tell whether the orthocenter of the triangle with the given vertices is inside, on, or outside the triangle. Then find the coordinates of the orthocenter. G(1,6), H(5,6), J(3,1)

inside; (3,5.2)

Compare m∠GHJ to m∠KLM (slide 10)

m∠GHJ ﹤ m∠KLM

Compare m∠RPS to m∠RSP (slide 15)

m∠PRS﹤m∠RSP

Compare m∠QPR to m∠QRP (slide 15)

m∠QPR﹥m∠QRP

Compare m∠QRP to m∠SRP (slide 15)

m∠QRP ﹤ m∠SRP

Use the diagram on slide 20: If RQ = RS and QT is greater than ST, then how does ∠QRT compare to ∠SRT?

m∠QRT is greater than m∠SRT

Compare m∠RSP to m∠RPS (slide 15)

m∠RSP = m∠RPS

PZ and PY are angle bisectors of triangle WYZ. Find the measure of ∠WZP and the distance from P to Z (slide 4)

m∠WZP = 46°; distance from P to Z = 16

Tell whether a triangle can have sides with given lengths: 14,18,32

no

Tell whether a triangle can have sides with given lengths: 2,9,12

no

Tell whether the orthocenter of the triangle with the given vertices is inside, on, or outside the triangle. Then find the coordinates of the orthocenter. K(-8,5), L(-6,3), M(0,5)

outside; (-6,-1)

Point D is the incenter of triangle LMN. Find the value of x. (slide 19)

x = 5

Tell whether a triangle can have sides with given lengths: 103,41.9,62.5

yes

Tell whether a triangle can have sides with given lengths: 4,7,10

yes

List the angle of triangle JKL in order from least to greatest: J(-3,-2), K(3,6), L(8,-2)

∠J, ∠L, ∠K

List the angle of triangle JKL in order from least to greatest: J(10,-4), K(5,3), L(2,-8)

∠L, ∠K, ∠J