A Special Point

ID: vilob-fanoj
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Geometry
Grade: 9-12
Standards: HSG-C.A.3HSG-CO.C.9HSG-SRT.B.5HSG-CO.C.10
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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?

A template for answering this question. Ask your instructor for an alternative.
Point and Angle

Here is an angle BACBAC with 2 different sets of markings.

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2) Point EE is the same distance away from each side of angle BACBAC. Are angles EABEAB and EACEAC congruent?

True or false? Write below.

3) Explain your reasoning.

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

5) Explain your reasoning.

What If There Are Three Sides?

Two angle bisectors have been constructed in triangle ABCABC. They intersect at point GG.

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

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7) How do the distances from point GG to sides ABAB and BCBC compare?

a)

The distance from point G to side ABAB is greater than the

distance from point G to BCBC.

b)

The distance from point G to side ABAB is less than the

distance from point G to BCBC.

c)

The distance from point G to side ABAB is equal to the

distance from point G to BCBC.

d)

There is not enough information to answer the question.

8) Explain your reasoning.

9) How do the distances from point GG to sides ACAC and BCBC compare?

a)

The distance from point G to side ACAC is greater than

the distance from point G to BCBC.

b)

The distance from point G to side ACAC is less than

the distance from point G to BCBC.

c)

The distance from point G to side ACAC is equal to

the distance from point G to BCBC.

d)

There is not enough information to answer the question.

10) Explain your reasoning.

11) Will the third angle bisector pass through point GG?

True or false? Write below.

12) Explain your reasoning.