Page 241 - ABCTE Study Guide_Neat

Now we can continue to verify that parallelogram ABCD above is a square.
So far we know:

• It has four sides.
• Its opposite sides are parallel.
• It has four right angles.

All we need to do now is measure the lengths of the sides. The opposite sides of a parallelogram are
congruent, so all we need to do is measure two adjacent sides.

We’ll measure the lengths of and . The length of a horizontal line segment equals the difference
between the x-coordinates. The endpoints of are A (–1, 3) and B (3, 3), so the difference between the x-
coordinates is 3 – (–1), or 4. Distance must be positive, so if we had found the difference to be –1 – (3), or –4,
we would still call the distance 4. So AB = 4. Thus, CD is also equal to 4.

The length of a vertical line segment equals the difference between the y-coordinates. The endpoints of
are B (3, 3) and C (3, –1), so the difference between the y-coordinates is –1 – (3), or –4.

So BC = 4. Thus AD, is also equal to 4.

We’ve shown that all sides of ABCD have the same length, so they’re all congruent. Therefore, ABCD is a
square.

Review

• A coordinate plane is formed by two perpendicular number lines that intersect at their
points of origin.
• You can use a coordinate plane to measure geometric figures.
• Protractors are used to measure angles.
• The length of a horizontal line segment equals the difference between the x-
coordinates. The length of a vertical line segment equals the difference between the y-
coordinates.

Measuring Triangles

Lesson Objective

In this next section, we’ll examine some components of a triangle and review the methods to
determine the perimeter and area of triangles.

We’ll also refresh your memory about the Pythagorean Theorem (and Pythagorean triples) and delve
into some basic trigonometry.

Previously Covered

Protractors are used to accurately measure and construct angles.

The length of a horizontal line segment equals the difference between the x-coordinates

The length of a vertical line segment equals the difference between the y-coordinates.