Question

learning targets

• i can visually determine if two lines are perpendicular
• i can determine if two lines are perpendicular.
• i can verify the intersection of a line perpendicular to a given line that passes through a given point.

indigo 1: perpendicular sides

1. which shapes have sides that are perpendicular to one another?

a. pentagon diagram b. rectangle diagram
c. right triangle diagram d. parallelogram diagram

1. mark the perpendicular sides. how would you explain the word perpendicular to a sixth grader?
2. draw a pentagon (five - sided polygon) that has one pair of perpendicular sides. then, compare your drawing with your classmates’ drawings. do your shapes look identical?

Explanation:

Question 1:

Step1: Recall perpendicular sides definition

Perpendicular sides are sides that intersect at a right angle ($90^\circ$).

Step2: Analyze each shape

• Shape A (pentagon): Its sides meet at angles that are not right angles (internal angles of a regular pentagon are $108^\circ$), so no perpendicular sides.
• Shape B (rectangle): All adjacent sides are perpendicular (intersect at $90^\circ$) since a rectangle has four right angles.
• Shape C (right triangle): The two legs of the right triangle are perpendicular (they form the right angle).
• Shape D (parallelogram): Its adjacent sides are not perpendicular (unless it's a rectangle, which this isn't), as parallelograms have adjacent angles that are supplementary but not necessarily $90^\circ$.

To mark perpendicular sides, look for sides that form a right angle (like the corner of a square or rectangle, or the legs of a right triangle). To explain "perpendicular" to a sixth - grader, say: "Imagine two lines (or sides) that meet like the corner of a rectangle or a square, where they form a square corner (a right angle, $90^\circ$). If you put a square at the corner where they meet, all the square's corners would fit perfectly."

Step1: Draw a pentagon with one pair of perpendicular sides

Start by drawing a right angle (two perpendicular segments). Then, attach three more segments to form a five - sided figure. For example, draw a vertical segment, a horizontal segment (perpendicular to the vertical one), then draw three more segments to connect the ends and form a pentagon.

Step2: Compare with classmates' drawings

Since there are many ways to draw a pentagon with one pair of perpendicular sides (the other three sides can be of different lengths and angles), the shapes will not look identical.

Answer:

B and C (the rectangle and the right triangle)

Question 2: