- If so, help the students to expand their thinking to see the other properties of the figure as well.
- Ask “What do you notice about the opposite sides of the figure?”
- Answer- They are congruent and parallel.
- Ask “What do you notice about the opposite angles?”
- Answer- They are also congruent.
- Ask- “Which angles are supplementary?”
- For this answer, have the students demonstrate the answer by using a protractor.
- Ask- “How can you use the diagonals of the shape to figure out the number of degrees in this figure?”
- Students should be using triangles for this.
III.MeetingObjectives
- Students will describe the relationships between opposite sides in a parallelogram.
- Students will describe the relationship between opposite angles in a parallelogram.
- Students will describe the relationship between consecutive angles in a parallelogram.
- Students will describe the relationship between the two diagonals in a parallelogram.
IV.NotesonAssessment
- Assessment for this lesson is completed as the students work through each step of the activity.
Proving Quadrilaterals are Parallelograms
I.SectionObjectives
- Prove a quadrilateral is a parallelogram given congruent opposite sides.
- Prove a quadrilateral is a parallelogram given congruent opposite angles.
- Prove a quadrilateral is a parallelogram given that the diagonals bisect each other.
- Prove a quadrilateral is a parallelogram if one pair of sides is both congruent and parallel.
II.ProblemSolvingActivity-IsitreallyaParallelogram?
- For this activity, students will need to cut two strips of paper that are the same length and two strips that aren’t.
- Then have the students attach the four strips of paper together at the ends with fasteners.
- This will form a quadrilateral.
- Explain to the students that some quadrilaterals are parallelograms and some aren’t.
- Then divide the students into groups.
- Students need to come up with ways to demonstrate the following points using their moveable figures.
- These points will help students to see how to prove that a quadrilateral is a parallelogram or that the shape that
they have created is NOT a parallelogram.
- Prove a point about opposite sides.
- Prove a point about opposite angles.
- Demonstrate the Supplement Theorem.
- Show how the number of degrees in a quadrilateral is the same as a parallelogram by using the Triangle
Sum Theorem.
- Show how the number of degrees in a quadrilateral is the same as a parallelogram by using the Triangle
- When students are finished working in their groups, give them time for each group to demonstrate one point
to the rest of the class. - Ask students to write what they have learned in their notebooks.
III.MeetingObjectives
Chapter 5. Geometry TE - Problem Solving