Les 9.3b Converse of Angle Bisector Theorem
WARM UP
Apply the Angle Bisector Theorem to answer the following Questions:
Conditional and Converse Statements
A conditional statement is written in the form of 'If hypothesis, then conclusion'. Example: If it rains heavily, then the school is closed'. A converse statement is just opposite of a conditional statement. To write a converse statemente from a given conditional statement we need to swap (reverse) the hypothesis and the conclusion. Thus, 'If conclusion, then hypothesis' represents the converse of 'If hypothesis, then conclusion'. Converse of the above statement is 'If the school is closed, then it is raining heavily. The validity (being Ture or False) of the conditional and converse statements depends on many factors. They both or one or none of them may be Ture or False. The Angle Bisector Theorem we learned yesterday is a conditional statement we explored to be ture always. Can you write the converse of the Angle Bisector Theorem?
CLASSWORK:
- You have been given an angle ABC.
- We are going to explore, if the converse of Angle Bisector Theorem is ture?
- So we need to start with our hypothesis, find a point F in the interior of angle ABC so that it is equidistant from sides BA and BC, and then check if the ray FB (connecting the point F and vertex B) bisects the angle ABC.
- Use 'Point on Object' tool to plot point D on side BA and point E on side BC.
- Use 'Perpendicular line' tool to draw lines perpendicular to BA at D and perpendicular to BC at E.
- Use 'Intersect' tool to find the intersection of the two perpendicular lines drawn above to find the point of intersection 'F'.
- Now, use 'Angle' measure tool to measure the angles BDF and angle FEB, each should be a right angle.
- Use 'Distance or Length' tool to measure the lengths of segments DF and EF, they may not be equal.
- According to the Converse statement we wrote, the point F to be equidistant from side BA and side BC. So, use the 'Move' tool to move the perpendicular line EF or line DF or both so that the lengths of segments DF and EF become equal (In otherwords segments DF and EF become congruent).
EXPLORATION - 1
EVALUATION: Does ray FB bisects the angle ABC?
To evaluate the conclusion, follow the direction below:
What did you observe?
Are the measures of angle FBA and angle CBF equal? Are they congurent?
Is the converse of Angle Bisector Theorem Ture?
Be elaborative in your response.
EXIT SLIP:
