Lesson 5-2/3: Lines in Triangles Relationships

Lesson 5-2/3: Lines in Triangles Relationships

DG, EG, and FG are the perpendicular bisectors of ∆ABC. Find GC.

G is the circumcenter of ∆ABC. By the Circumcenter Theorem, G is equidistant from the vertices of       

∆ABC.

Fill in the Blanks

Fill in the Blanks

MP and LP are angle bisectors of ∆LMN. Find the distance from P to MN.

P is the incenter of ∆LMN. By the Incenter Theorem, P is equidistant from the sides of ∆LMN.

The distance from P to LM is 5. So the distance from P to MN is also 5.

MP and LP are angle bisectors of ∆LMN. Find m∠PMN.

m∠MLN = 2m∠PLN 

m∠MLN = 2(50°) = 100°

m∠MLN + m∠LNM + m∠LMN = 180° 

100 + 20 + m∠LMN = 180 

m∠LMN = 60° 

m∠PMN = .5 (m∠LMN)

m∠PMN = .5 (60°)

m∠PMN = 30°

Fill in the Blanks

Multiple Choice

QX and RX are angle bisectors of ∆PQR. Find m∠PQX.

• 104°

• 52°

• 24°

• 26°

For the Centroid Theorem

• In the notes, the definition for this theorem states that the shorter portion of the median is 1/3 the length of the whole median

• Therefore the longer portion of the median would be 2/3 the length of the whole median.

• This will be helpful when trying to find the lengths.

In ∆LMN, RL = 21 and SQ =4. Find LS.

*Need to find Longer Portion of Median

LS = (2/3) RL

LS = (2/3) (21)

LS = 14

In ∆LMN, RL = 21 and SQ =4. Find NQ.

*Need to find Full length of median but given the shorter portion

SQ = (1/3) NQ

4 = (1/3) NQ

12 = NQ

Multiple Choice

In ∆JKL, ZW = 7, and LX = 8.1. Find KW.

• 21

• 7

• 14

Multiple Choice

In ∆JKL, ZW = 7, and LX = 8.1. Find LZ.

• 8.1

• 2.7

• 5.4