1. 5.2 - Special segments in triangles

2. Perpendicular bisector of a triangle

3. Perpendicular bisector of a triangle3
Every triangle has __________ perpendicular bisectors.
Does one of the endpoints of a perpendicular bisector have to be a vertex of the triangle? ________
(one for each side of the triangle)
Yes or no? What do you think? Look at the diagrams above to answer.

4. Angle bisector of a triangle
bisects one of the angles of the triangle 3
Yes!
Angle bisectors must go through the vertex of the angle. The vertex of the angle and the vertex of the triangle are the same point!

5. median 3 Yes or no? What does the definition say?
endpoints are a vertex and the midpoint of the opposite side
is 𝑺𝑩 3
Yes or no? What does the definition say?
Yes, a ⊥ bis. can be a median. Name the triangle and the segment where this happens on this page.

6. altitude
a vertex that is ⊥ to the opposite side or to the line containing
the opposite side
⋆⋆In right triangles, two of the altitudes are the legs of the triangles.

7. altitude
A segment from a vertex that is ⊥ to the opposite side or to the line containing the opposite side
⋆⋆These can be tricky – two of the altitudes are segments OUTSIDE of the triangle. We have to extend the sides to be able to draw the altitude.

8. Altitude 3 Yes, this happens in ∆ _______ with segment ____
Yes or no? Look back at the altitudes in each case of acute, right, and obtuse triangles. 3
Yes or no?
What does the definition say?
Altitudes are sometimes inside the ∆, while a ⊥ bis. always are inside the ∆
Altitudes sometimes goes through the midpoint of a side, while a ⊥ bis. always goes through the midpoint of a side
Altitudes always has the vertex as an endpoint, while a ⊥ bis. sometimes (and very rarely) has the vertex as an endpoint
Yes, this happens in ∆ _______ with segment ____

9. Copy the bullet points and fill in these blanks with theorems/terms
∆𝑇𝑅𝑄≅∆𝑇𝑆𝑄 by __________________________
∠𝑅𝑇𝑄≅∠𝑆𝑇𝑄 by ______________ ⇒ 𝑇𝑄 is a ____________________ of ∆𝑇𝑅𝑆
∠𝑅𝑄𝑇≅∠𝑆𝑄𝑇 by ______________ ⇒ 𝑇𝑄 ⊥ 𝑅𝑆 ⇒ 𝑇𝑄 is a ____________________ of ∆𝑇𝑅𝑆
Copy the bullet points and fill in these blanks with theorems/terms
all the same segment
all the same segment

10. Closure question – complete on your warm-up paper
Given F is the midpoint of 𝐵𝐶 and ∠𝐴𝐷𝐸≅∠𝐶𝐴𝐸.
1. Segment AD is a(n) _________
2. Segment AE is a(n) __________
3. Segment AF is a(n) __________
4. Line GF is a(n) __________