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VOCABTry seeing it from my angle

Don't be so obtuse, you know I'm right

I sent Roy to the Median of the line

Don't act all high and mighty, some things are > you

This segment is formed when connecting the midpoints of two sides of a triangle.

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What is a Midsegment

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This is the point where three or more lines, segments, or rays intersect.

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What is the point of concurrency

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What is an Orthocenter, Circumcenter, Centroid, and Incenter?

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Points of concurrency for altitudes, perpendicular bisectors, medians, and angle bisectors (respectively).

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Where are Circumcenters, Incenters, Centroids, and Orthocenters located?

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Circumcenters and Orthocenters's locations depend on the type of triangle formed. Acute triangles have the circumcenter and orthocenter inside. Right triangles have the circumcenter and the orthocenter located on the triangle. Obtuse triangles have the circumcenter and orthocenter outside the triangle.Incenters and Centroids are always located inside a triangle.

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Match the correct segment with its corresponding property

1. Perpendicular Bisectors

2. Medians

3. Midsegment

4. Angle Bisectors

(a)

(c)

(b)

(d)

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1. C2. D3. A4. B

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WZ = 9

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Find the value of x

(6x)ο

(2x + 16)ο

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X = 4

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A

C

D

F

G

B

E

8

6

Point D is the incenter of ΔABC. Find the value of FD.

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FD = 8

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Is DA = DC? Explain.

A

B

CD

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No, we do not know that DA is perpendicular to AB nor do we know that DC is perpendicular to BC.

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Find the value of x that makes N the incenter of the triangle.

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x = 6

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List the sides and angles in order from smallest to largest.

LK

J

32ο

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Angles: L, K, JSides: KJ, LJ, KL

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Is it possible to construct a triangle with side lengths of 1, 6, and 4? Explain why or why not.

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It is not possible, since the sum of any two sides should be greater than the last side. Since 1 + 4 is not greater than 6, a triangle can not be formed.

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What conclusion can be made about the triangles below?

M

S

D

A

95ο 98ο

**Figures not drawn to scale

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AD > AM

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Describe the possible values of x

G

HF

18

8

4x + 2

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2 < x < 6

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x + 3

1245ο

115ο

12

3x + 1

Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe a restriction on the value of x

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x > 1

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W

X

R S

T

Y

In ΔWXY, R, S, and T are midpoints of the sides

What is RS parallel to?

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WY

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If RT = 7, then XY =

W

X

R S

T

Y

In ΔWXY, R, S, and T are midpoints of the sides

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14

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What is the value of x?

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7

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Identify the coordinates for point R and point T.

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R (h, h) and T(h,0)

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W

X

R S

T

Y

In ΔWXY, R, S, and T are midpoints of the sides

If ST = 3.5x + 6 and WX = 3x + 36, then ST =

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ST = 27

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Find the value of PN.

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PN = 6

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If LP = 6, what is the value of LZ?

LZ = 18

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Daily Double

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Find the coordinates of the centroid of a triangle with the given vertices: R (-3,6), S(-5, 2), T(-7, 10)

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(-5, 6)

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Point P is the centroid of ΔXYZIf ZP = 3x + 7 and ZL = 6x, what is the value of x?

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x = 7

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Point P is the centroid of ΔXYZIf YP = 10x - 4 and YN = 12x + 18, what is the value of segment YP?

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YP = 76

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