Drawing Conclusions from Rational Expressions

The video tutorial focuses on drawing logical conclusions using a five-step procedure. It provides examples involving congruent angles, perpendicular rays, congruent segments, bisecting angles, assumptions from diagrams, and midpoints. The lesson concludes with homework instructions for further practice.

What is the first step in the five-step procedure for drawing logical conclusions?

• Look for key words and symbols

• Memorize the theorems, definitions, and postulates

• Draw a conclusion and give a reason

• Think of all theorems, definitions, and postulates that involve key words

Which page in the textbook can you refer to for the five-step procedure?

• Page 74

• Page 72

• Page 70

• Page 76

What should you do in step 3 of the five-step procedure?

• Think of all theorems, definitions, and postulates that involve key words

• Memorize the theorems, definitions, and postulates

• Draw a conclusion and give a reason

• Decide which theorem allows you to draw a conclusion

In example one, what conclusion can be drawn if angle ABD is congruent to angle DBC?

• Ray BD trisects angle ABC

• Ray BD bisects angle ABC

• Ray BD forms a right angle

• Ray BD is perpendicular to angle ABC

What is the reason given for the conclusion in example one?

• If a line bisects a segment, then it divides the segment into two congruent segments

• If two points divide a segment into three congruent segments, then they trisect the segment

• If two rays are perpendicular, then they form a right angle

• If a ray divides an angle into two congruent angles, then the ray bisects the angle

In example two, what conclusion can be drawn if ray GK is perpendicular to ray GR?

• Angle KGR is a right angle

• Angle KGR is an obtuse angle

• Ray GK bisects angle GR

• Ray GK trisects angle GR

What is the reason given for the conclusion in example two?

• If a line bisects a segment, then it divides the segment into two congruent segments

• If two points divide a segment into three congruent segments, then they trisect the segment

• If two rays are perpendicular, then they form a right angle

• If a ray divides an angle into two congruent angles, then the ray bisects the angle

In example three, what conclusion can be drawn if segment LN is congruent to segment MO and segment OP?

• Points M and O bisect segment LP

• Points M and O trisect segment LP

• Points M and O are midpoints

• Points M and O form a right angle

What is the reason given for the conclusion in example three?

• If a line bisects a segment, then it divides the segment into two congruent segments

• If two points divide a segment into three congruent segments, then they trisect the segment

• If two rays are perpendicular, then they form a right angle

• If a ray divides an angle into two congruent angles, then the ray bisects the angle

What can be assumed from a diagram showing a straight angle?

• The angle is a straight angle

• The angle is a right angle

• The angle is trisected

• The angle is bisected