AnswersOC - LCISD - Geometry BCentroid and Orthocenter

Triangle Congruence: SAS Answers

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Triangle A B C is shown. Lines are drawn from each point to the opposite side and intersect at point D.

Question illustration
A
Point D can be the orthocenter because it is the point of intersection of three segments coming from the vertices of the triangle.
B
Point D can be the orthocenter because each vertex angle appears to be bisected.
C
Point D cannot be the orthocenter because the orthocenter of an obtuse triangle is located outside the triangle.
D
Point D cannot be the orthocenter because the orthocenter of an obtuse triangle is located on the perimeter of the triangle.
2
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In which figure is point G an orthocenter?

A
Triangle A B C is a right triangle. Lines are drawn from each point to the opposite side and intersect at point G.
Option A
B
Triangle F D E is shown. Lines are drawn from each point to the opposite side and intersect at point G. The lines cut each side into 2 equal parts.
Option B
C
Triangle L M N is shown. Lines are drawn from each point to the opposite side and intersect at point G. Each angle has a different measure.
Option C
D
Triangle H J K is shown. Lines are drawn from each point to the opposite side to form right angles and the lines intersect at point G.
Option D
3

A centroid is the intersection of three

A
altitudes in a triangle.
B
perpendicular bisectors in a triangle.
C
angle bisectors in a triangle.
D
medians in a triangle.
4

In the diagram, GB = 2x + 3..

Question illustration
A
5 units
B
10 units
C
15 units
D
30 units
5

The steps shown can be used to prove that the medians of a triangle meet at a point.1. Define segments BD and CE as medians of triangle ABC.2. Write linear equations for and .3. Use a system of linear equations to solve for the coordinates of intersection point G.4. Write the equation of .5. Write an expression for the midpoint of BC, point F. 6. Show that point F lies on .7. ?

Question illustration
A
Write a linear equation for each side of the triangle.
B
Write an expression for the midpoint of AC and BC.
C
Show that AF is congruent to BD and CE.
D
Show that AF is the median of BC.
6

In which type of triangle is the orthocenter on the perimeter of the triangle?

A
a right triangle
B
an acute triangle
C
an obtuse triangle
D
an equilateral triangle
7

An orthocenter is the intersection of three

A
angle bisectors in a triangle.
B
altitudes in a triangle.
C
medians in a triangle.
D
perpendicular bisectors in a triangle.
8

Triangle D E F is shown. Lines are drawn from each point to the opposite side and intersect at point G. Line segments D C, E B, and F A are formed and cut each side into 2 equal parts.

Question illustration
A
5 cm
B
10 cm
C
15 cm
D
20 cm
9

In triangle NLM, point S is the centroid, QS = (3x – 5) cm, and NS = (4x) cm.

Question illustration
A
5 cm
B
10 cm
C
20 cm
D
30 cm
10

Point G is the centroid of triangle ABC. The length of segment CG is 6 units greater than the length of segment DG.

Question illustration
A
6 units
B
12 units
C
18 units
D
24 units

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