Warm Up Complete each statement. 1. A triangle with an angle that measures 90 is a_______ triangle. right 2. A quadrilateral with exactly one pair of parallel sides is a ____________. trapezoid 3. A quadrilateral with two pairs of parallel sides is a ____________. parallelogram 4. A rhombus with 4 right angles is a ____________. square

Problem of the Day What type of polygon am I? My opposite angles have equal measure. I do not have a right angle. All my sides are congruent. rhombus

Learn to identify polygons and midpoints of segments in the coordinate plane.

Vocabulary midpoint

In computer graphics, a coordinate system is used to create images, from simple geometric figures to realistic figures used in movies. Properties of the coordinate plane can be used to find information about figures in the plane, such as whether lines in the plane are parallel.

Additional Example 1A: Using Coordinates to Classify Quadrilaterals Graph the polygons with the given vertices. Give the most specific name for the polygon. A(0, –2), B(3, 3), C(3, –2) Step 1: Classify the polygon by its angles. C is a right angle, so triangle ACB is a right triangle.

Additional Example 1A Continued Step 2: Classify the triangle by its sides. Find the length of each side. AC = |3 – 0| = 3 BC = |–2 – 3| = 5 The triangle has no congruent sides, so it is scalene. Triangle ACB is a right scalene triangle.

Additional Example 1B: Using Coordinates to Classify Quadrilaterals Graph the polygons with the given vertices. Give the most specific name for the polygon. L(2, 1), M(5, 1), N(5, –1), P(2, –1) Examine the sides of the quadrilateral. LM and PN are parallel. LP and MN are parallel. The quadrilateral is a rectangle because it has two sets of parallel sides and the sets of parallel sides are different lengths.

Examine the sides of the quadrilateral. Check It Out: Example 1 Graph the polygons with the given vertices. Give the most specific name for the polygon. Q(–2, 3), R(1, 5), S(1, –2), T(–2, –4) Examine the sides of the quadrilateral. QT and RS are parallel. QR and TS are parallel. The quadrilateral is a parallelogram because it has two sets of parallel sides and the sets of parallel sides do not form 90 angles.

Additional Example 2A: Finding the Coordinates of a Missing Vertex Find the coordinates of each missing vertex. Triangle ABC has a right angle at C and AC = 2. Find one set of possible coordinates for A. Since BC is horizontal, AC must be vertical for the triangle to have a right angle at C. (4, 0) or (4, –4)

Additional Example 2B: Finding the Coordinates of a Missing Vertex Find the coordinates of each missing vertex. Quadrilateral LMNP is a parallelogram. Find the coordinates of N. MN must be vertical and the same length as LP. (1, 0)

Check It Out: Example 2 Find the coordinates of each missing vertex. Triangle ABC has a right angle at B and AB = 3. Find one set of possible coordinates for A. Since BC is horizontal, AB must be vertical for the triangle to have a right angle at B. (1, 1) or (1, –5)

The midpoint of a segment is the point that divides the segment into two congruent segments.

Additional Example 3: Finding the Coordinates of a Midpoint Find the coordinates of midpoint AB. Use the formula. The endpoints are A (0, 2) and B(3, 5). Simplify. The coordinates of the midpoint M is

Find the coordinates of midpoint LM. Check It Out: Example 3 Find the coordinates of midpoint LM. Use the formula. The endpoints are L (–1, 3) and M(2, 1). Simplify. The coordinates of the midpoint M is

Lesson Quiz: Part I 1. Graph the polygon with vertices A(0, 1), B(1, 3), C(3, 3), and D(5, 1). trapezoid

2. Quadrilateral LMNP is a parallelogram. Find the coordinates of P. Lesson Quiz: Part II 2. Quadrilateral LMNP is a parallelogram. Find the coordinates of P. 3. Find the coordinates of the midpoint MN. (4, 1) (5, 2.5)

Lesson Quiz for Student Response Systems 1. Graph the polygon with vertices A(1, 1), B(1, 3), C(3, 3), and D(3, 1). Give the most specific name for the polygon. A. square B. rectangle C. parallelogram D. trapezoid 19

Lesson Quiz for Student Response Systems 2. Find the coordinates of the midpoint CD. A. (2, 2) B. (2, 1) C. (4, 2) D. (4, 1) 20