Unit 4 - Points of Concurrency - Orthocenter

Question 1

How do you construct a perpendicular line on a random point on a line (4)

Answer 1

1. Open compass to any size
2. Put pointy part of your compass on the point and draw a circle
3. Draw two endpoints on the two intersections of the line
4. Draw a perpendicular bisector

Question 2

How do you construct a perpendicular line on a point above or below a random line? (3)

Answer 2

1. Construct a REFLECTION
2. Draw a line connecting pre - image to image
3. You created your perpendicular line!

Question 3

Definition of altitude in terms of a triangle (4)

Answer 3

1. A segment
2. Connecting the vertex angle
3. Point on the opp. side of the triangle
4. That’s perpendicular to each other

Question 4

What do you add to the square root of a perfect square?

Answer 4

REMEMBER THE + AND -

Question 5

What are the four things the altitude of an isosceles and equilateral triangle serve as?

Answer 5

1. Median (midpoint of opp. side)
2. Perpendicular Bisector
3. Angle Bisector
4. Line of Reflection/Line of Symmetry

Question 6

How do you construct the altitude of the triangle? (2)

Answer 6

1. Perform a reflection on the vertex angle
2. Connect pre - image to image

Question 7

Definition of the Orthocenter (2)

Answer 7

1. Point of Concurrency
2. Altitudes of Triangle Meet

Question 8

What’s the difference between the median and altitudes?

Answer 8

Altitude is a PERPENDICULAR line
Median involves the MIDPOINT

Question 9

Where is the orthocenter located for the acute, obtuse and right triangle?

Answer 9

1. Acute - Inside
2. Obtuse - Outside
3. Right - 90 degree (vertex) Angle

Question 10

How do you construct the orthocenter? (2)

Answer 10

1. Draw two altitudes
2. Where altitudes meet is the orthocenter