# A Special Point

ID: vilob-fanoj
Illustrative Mathematics, CC BY 4.0
Subject: Geometry
Standards: HSG-C.A.3HSG-CO.C.9HSG-SRT.B.5HSG-CO.C.10

12 questions

# A Special Point

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##### Notice and Wonder: Salt Pile

1) In the image, a cardboard triangle has been balanced on the top of bottle. Salt has been poured slowly onto the triangle until after the triangle has reached capacity.

What do you notice? What do you wonder?

##### Point and Angle

Here is an angle ﻿$BAC$﻿ with 2 different sets of markings.

2) Point ﻿$E$﻿ is the same distance away from each side of angle ﻿$BAC$﻿. Are angles ﻿$EAB$﻿ and ﻿$EAC$﻿ congruent?

True or false? Write below.

4) Point ﻿$H$﻿ is on the angle bisector of angle ﻿$BAC$﻿. What can you prove about the distances from ﻿$H$﻿ to each ray?

##### What If There Are Three Sides?

Two angle bisectors have been constructed in triangle ﻿$ABC$﻿. They intersect at point ﻿$G$﻿.

6) Sketch segments that show the distances from point ﻿$G$﻿ to each side of the triangle.

7) How do the distances from point ﻿$G$﻿ to sides ﻿$AB$﻿ and ﻿$BC$﻿ compare?

a)

The distance from point G to side ﻿$AB$﻿ is greater than the

distance from point G to ﻿$BC$﻿.

b)

The distance from point G to side ﻿$AB$﻿ is less than the

distance from point G to ﻿$BC$﻿.

c)

The distance from point G to side ﻿$AB$﻿ is equal to the

distance from point G to ﻿$BC$﻿.

d)

There is not enough information to answer the question.

9) How do the distances from point ﻿$G$﻿ to sides ﻿$AC$﻿ and ﻿$BC$﻿ compare?

a)

The distance from point G to side ﻿$AC$﻿ is greater than

the distance from point G to ﻿$BC$﻿.

b)

The distance from point G to side ﻿$AC$﻿ is less than

the distance from point G to ﻿$BC$﻿.

c)

The distance from point G to side ﻿$AC$﻿ is equal to

the distance from point G to ﻿$BC$﻿.

d)

There is not enough information to answer the question.

11) Will the third angle bisector pass through point ﻿$G$﻿?