Another kind of Bisector

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Another Kind of Bisector

Angle Bisector

In this activity you will use algebra to prove some geometric principles about the bisector of an angle formed by two intersecting lines.

Before attempting to do this homework review your work on POW 2: Equally Wet.

Read about perpendicular bisector and angle bisector (see page 97 of your book). Be prepared to share those definitions.

Also, review the definition of:

Straight angle

Collinear

Question 1

This question is basically the same as question 2a of your homework 9: Perpendicular or Vertical, so you should have no problem answering it.

Remember:

Vertical angles are congruent (opposite angles).

Supplementary angles add up to 180 degrees.

That will be enough to explain your answer to question 1.

Question 2a

Again, you will need the following tdefinitions to explain your answer.

Vertical angles are congruent (opposite angles).

Supplementary angles add up to 180 degrees.

An angle bisector is a ray that splits (divide) an angle into two equal parts.

Start by showing that the sum of PAC, CAQ, and QAD is 180 degrees.

Explain the value of every angle by quoting one of the previous definition listed above.

Now, use the definition of collinear and the fact that:

<PAC + <CAQ + QAD = 180 degrees

to state that the two lines are collinear.

Question 2b

Use the same reasoning to answer question 2a.

Question 2c

Use the same reasoning to answer question 2c, but make sure that you prove that < PAC + < CAQ = 90 degrees, etc..

Question 3

What is < PAC in term of x?

What is <CAD?

The reasoning in question 3 is identical to that for question 2 but instead of :

< BAC = 70 degrees,

you have to generalize using:

< BAC = x

Go ahead and follow all the steps as in question 2a using x instead of 70.

Notice that <PAC was equal to 70 ÷2; now it should be <PAC= x ÷2

Go ahead and finish your answer. Be ready to share your solution in class.

Mr. Lora

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