5.2 - Special segments in triangles

Perpendicular bisector of a triangle

Perpendicular bisector of a triangle 3 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.

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!

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.

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.

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.

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 ____

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

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) __________