eQuizShow

Geo. Ch.5

Center Names

Question: The name of this triangle center is formed by the intersection of the three altitudes of a triangle.
Answer: Orthocenter

Question: This _________center is the center of a circle around a triangle
in which the three vertices of the triangle are located on the circle.
Answer: Circumcenter.

Question: What center is constructed in the sketch

Answer: Orthocenter.

Question: What triangle center is constructed in the sketch:

Answer: Circumcenter

Question: What triangle center is constructed in the sketch:

Answer: Centroid.

3 segments used

Question: The Incenter of a triangle is formed by the intersection of the three _________.
Answer: Angle Bisectors

Question: What three segments are used to construct the orthocenter of a triangle?
Answer: The altitudes of a triangle.

Question: The three segments used to construct a Circumcenter are the segments that connect the
midpoint of a side and is perpendicular to that side.
(T/F)
Answer: True.

Question: If you multiply this segment by 2/3, you get the distance from the vertex to the centroid of the triangle.
Answer: Median.

Question: To construct this segment,
which connects from the vertex to the opposite side of the triangle at 90 degrees,
you may have to extend the opposite side of the triangle in order to construct it.
Answer: The altitude.

Triangle Center Locations

Question: T/F The centroid can be located outside of a triangle.
Answer: False. The centroid is always located inside a triangle.

Question: Name the center that is constructed in the image below.

Answer: Angle bisectors are used to construct the incenter of the triangle.

Question: Name the two triangle centers that are always located "inside" the triangle.
Answer: Incenter and Centroid.

Question: Where is the orthocenter located on any right triangle? Be specific with your answer.

Answer: On the vertex of the 90 degree angle (or on the vertex of the right angle).

Question: List all the triangle centers that can be constructed "outside" of the triangle.
Answer: Circumcenter and Othocenter.

Something Special

Question: If you construct the circumcenter for an acute triangle, then this center can be used to construct a circle that is located where, in relation to the triangle?
Answer: The circle will be located outside the triangle, with the three vertices of the triangle located on the circle.

Question: This triangle center is also called the "center of gravity" of the triangle.
Answer: Centroid

Question: If you construct the circumcenter of an obtuse triangle, then this center will be located where in relation to the triangle?
Answer: Outside the triangle.

Question: To construct the circle that is located inside the triangle, the only segments needed are the angle bisectors. T/F
Answer: False. You also need to construct the perpendicular segment from the incenter to each side of the triangle.

Question: 2-part question:
1.) On what side of any right triangle is the circumcenter located?
2.) Where exactly on this side is the CC located?

Answer: The circumcenter is located on the midpoint of the hypotenuse for any right triangle.

Hodgepodge

Question: Describe what vertical angles are and how they are formed.
Answer: Vertical angles are formed by the intersection of two lines. Angles that are opposite each other are congruent and are called vertical angles.
There are two pairs of vertical angles when two lines intersect.

Question: Describe what the hinge theorem is.
Answer: If 2 sides of one triangle are congruent to 2 sides of another triangle and the included angle between the 2 congruent sides in the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is larger than the third side of the second triangle.

Question: Can the three side lengths 12, 18, 9 form the sides of a triangle?
Answer: Yes. 9+12>18

Question: What is the range for the possible side lengths of the third side of a triangle if two side lengths are 32cm and 48cm?
Answer: Third side range is: 16
Question: Sketch the following triangle and answer the question.
In triangle ABC, angle A is 43 degrees, angle B is 37 degrees, and angle C is 100 degrees.
List the side lengths in order from largest to smallest.
Answer: AB, BC, AC