# 5.3 Investigation 2

- Author:
- diego83720

## What are some Properties of Trapezoids?

Step 1: Use the two edges of your straightedge to draw parallel segments of unequal length. Draw two nonparallel sides connecting them to make a trapezoid.
Step 2: Use your protractor to find the sum of the measures of each pair of consecutive angles between the parallel bases. What do you notice about this sum? Share your observation with your group.
What I noticed about this sum is that it relates to the Quadrilateral Sum Conjecture that states, ''The sum of the measure of the four interior angles of any quadrilateral is 360.
Step 3: Copy and complete the conjecture
Trapezoid Consecutive Angles Conjecture
The consecutive angles between the bases of a trapezoid are supplementary.
Like Kites, isosceles trapezoids have one line of reflectional symmetry. Through what points does the line of symmetry pass?
The points the line of symmetry passes through is the midpoint of the pairs of parallel lines
Step 4: Use both edges of your straightedge to draw parallel lines. Using your compass construct two congruent, nonparallel segments. Connect the four segments to make an isosceles trapezoid.
Step 5: Measure each pair of base angles. What do you notice about the pair of base angles in each trapezoid? Compare your observations with others near you.
I noticed that the pair of base angles in each trapezoid are congruent.
Step 6: Copy and complete the conjecture.
Isosceles Trapezoid Conjecture
The base angles of an isosceles trapezoid are congruent.
What other parts of an isosceles trapezoid are congruent? Let's continue.
Step 7: Draw both diagonals. Compare their lengths. Share your observations with other near you.
The distance from the base angle to the concurrency of the diagonals are equal and so are the ones for the vertex angles.
Step 8: Copy and complete the conjecture
Isosceles Trapezoid Diagonals Conjecture
The diagonals of an isosceles trapezoid are congruent.