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Centroid and Orthocenter Answers

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What statements are true about the orthocenter of triangle JKL? Check all that apply.

A
The orthocenter is where the medians of the triangle intersect.
B
The orthocenter is where the altitudes of the triangle intersect.
C
The orthocenter will lie on triangle JKL.
D
Without constructing the orthocenter, it is impossible to know if it will be on, in, or outside the triangle.
E
To find the orthocenter, determine the midpoints of the triangle sides.
3

JK✔ L

A
J
B
K
C
✔ L
4

D✔ EF

A
D
B
✔ E
C
F
5

EF✔ LEKF

A
EF
B
✔ LE
C
KF
121151

What was the first in constructing the altitude WZ for triangle XYZ?

Answers:
Place the compass point at and draw an arc that intersects segment twice.:Z
Place the compass point at and draw an arc that intersects segment twice.:XY
121152

WZ✔ XYXZYZ

A
WZ
B
✔ XY
C
XZ
D
YZ
121153

Which step in the construction of the altitude assures that AD is perpendicular to EF?

A
Place the compass on vertex D and adjust the width so that the drawn arc goes past side EF.
B
Draw an arc to intersect side EF twice.
C
From each intersection point, draw an arc above side EF so that the two arcs cross.
D
Draw a line from vertex D to point A to create altitude AD.
121154

Which of the following is a correct step for constructing a median of triangle LMN?

A
Bisect side LN. Construct a line perpendicular to LN through vertex M.
B
Bisect the angle at vertex M. Extend the angle bisector to intersect side LN.
C
Bisect side LN. Construct a line segment through vertex M and the midpoint of side LN.
D
Bisect side LN and side MN. Construct a line segment connecting the two midpoints.
121155

Which of the following is a result of the construction of a median of a triangle?

A
An angle of the triangle is bisected.
B
A perpendicular segment is created from a vertex to the opposite side.
C
A side of the triangle is bisected.
D
The center of the triangle is found.
121156

Complete the statements.

Answers:
Point is the midpoint of side .:E
Point is the midpoint of side .:JK
To finish the construction, draw a segment from vertex to point .:L
To finish the construction, draw a segment from vertex to point .:E
Then, segment is a median of triangle JKL.:LE
121157

Complete the statements.

Answers:
Point is the midpoint of side .:E
Point is the midpoint of side .:JK
To finish the construction, draw a segment from vertex to point .:L
To finish the construction, draw a segment from vertex to point .:E
Then, segment is a median of triangle JKL.:LE

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