Ch5 ReTeach - KAP

Ch5 ReTeach

This will review the main question types on the test to allow you to better complete your test corrections & retest

Medians

• segment from vertex to opposite side's midpoint

• Ex. $\overline{HJ}$ 

• Since J is the midpoint of  $\overline{GI}$  , then  $\overline{IJ}\cong\overline{JG}$  

• Equation to set up:  $IJ=JG$  (part=part)

Multiple Choice

Which represents a median of

 $\Delta GHI?$  

•  $\overline{NI}$  

•  $\overrightarrow{HJ}$  

•  $\overline{KG}$  

•  $\overleftarrow{L}\overrightarrow{M}$  

Angle Bisectors

• Angle Bisector - from vertex and cuts vertex angle into two congruent parts

• Ex. $\overrightarrow{GL}$  

• Since  $\overrightarrow{GL}$  bisects  $\angle IGH$  , then  $\angle IGL\cong\angle LGH$  

• Equation:  $m\angle IGL=m\angle GLH$  (part=part)

Multiple Choice

Which represents an angle bisector of

 $\Delta GHI?$  

•  $\overline{NI}$  

•  $\overrightarrow{HJ}$  

•  $\overline{KG}$  

•  $\overleftarrow{L}\overrightarrow{M}$  

Perpendicular Bisectors

• segment from a midpoint at a right angle & does not have to include a vertex
  

• Ex. $\overleftarrow{J}\overrightarrow{M}$ 
  

• Since J is the midpoin. of  $\overline{GI}$  &  $\overline{GI}\perp\overleftarrow{J}\overrightarrow{M}$ ,  then  $IJ=JM$ ,  $m\angle AJI=90\degree$ , and  $m\angle AJG=90\degree$  

   $-$ 

Multiple Choice

Which represents a perpendicular bisector of

 $\Delta GHI?$  

•  $\overline{NI}$  

•  $\overrightarrow{HJ}$  

•  $\overline{KG}$  

•  $\overleftarrow{L}\overrightarrow{M}$  

Altitudes

• Altitude - from right angle to opposite vertex

• Ex. $\overline{KI}$  
  

• Since  $\overline{KI}\perp\overline{HG}$ , then  $m\angle IKH=90\degree$  and  $m\angle IKG=90\degree$   

Multiple Choice

Which represents an altitude of

 $\Delta GHI?$  

•  $\overline{NI}$  

•  $\overrightarrow{HJ}$  

•  $\overline{KG}$  

•  $\overleftarrow{L}\overrightarrow{M}$  

Most Missed #1

• Median extends from midpoint to opposite vertex

• Equation uses the fact that H is the midpoint of $\overline{EG}$   
  

• Therefore,  $EH=HG$  

Multiple Choice

Since there is a median, which equation could be used to solve for x?

• $x+18=9x+6$

• $x+18=2x+23$

• $2x+23=7x-2$

• $7x-2=9x+6$

Most Missed #1

• Use  $EH=HG$  for the equation

• Solve for x

Multiple Choice

Using the equation in the photo, what is the value of x?

• x = 2.3

• x = 4.2

• x = 1.5

• x = 5

Most Missed #1

• Once you have x=5,

• you can substitute it back in to get the length of any segment

•  $EH=\left(5\right)+18=23$  

•  $EH=2\left(5\right)+23=33$  

•  $HG=7\left(5\right)-2=33$  

•  $FG=9\left(5\right)+6=51$  

Most Missed #2

• Though it tells us that we have an altitude, our algebraic expression doesn't go with the right angle

•  $\overline{BE}$  is NOT an angle bisector

• We will use triangle angle sum to set up the equation

Multiple Choice

What is the sum of the interior angles in any triangle?

• 180

• 90

• 3

• 360

Most Missed #2

• Equation uses all interior angles in

   $\Delta DBC$  

• Solve for x

Multiple Choice

what is the value of x?

• 8

• 19

Most Missed #2 - Check your work

Most Missed #3

• W is a midpoint of $\overline{ZT}$  
  

• Therefore, $ZW=WT$  which both = 3

•  $XT=XZ+ZW+WT$  

•  $XT=12+3+3=18$  

Multiple Choice

Which point of concurrency is equidistant to each VERTEX in a triangle?

• centroid

• incenter

• circumcenter

• orthocenter

Multiple Choice

Which point of concurrency is equidistant to each SIDE in a triangle?

• centroid

• incenter

• circumcenter

• orthocenter

Multiple Choice

An incenter is the point where three __?__ intersect for any triangle?

• medians

• angle bisectors

• perpendicular bisectors

• altitudes

Label your picture with the given information first and mark congruent angles

Multiple Choice

What is the $m\angle KHM$ ?

• 15

• 30

• 27

• 33

• 54

Multiple Choice

What is the $m\angle IJM$ ?

• 15

• 30

• 27

• 33

• 54

Multiple Choice

What is the $m\angle MJN$ ?

• 15

• 30

• 27

• 33

• 54

Check your work

Most Missed #5

• Different ways to prove congruence: SSS, SAS, ASA, AAS, & HL

• HL can only be used with right triangles

• If it is a right triangle, then "SSA" turns into HL

Multiple Choice

What relationship proves triangle congruence between these two triangles

• SSS

• SAS

• ASA

• AAS

• HL

Multiple Choice

What relationship proves triangle congruence between these two triangles

• SSS

• SAS

• ASA

• AAS

• HL

You are done with the Reteach & time to complete the ReTest

log onto Canvas and complete "Chapter 5 Re-Test" to earn a maximum of a 75 back on your test