Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5...
-
Upload
martina-wheeler -
Category
Documents
-
view
215 -
download
0
Transcript of Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5...
![Page 1: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/1.jpg)
QuadrilateralsLesson 6-1
![Page 2: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/2.jpg)
Warm-up
![Page 3: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/3.jpg)
Warm-upSolve the following triangles using the
Pythagorean Theorem a2 + b2 = c2
95
12 9
8
8√3
![Page 4: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/4.jpg)
Warm-upFind the missing point given the following
information.
1. Point 1 (3, 8), Point 2 (5, 12), Midpoint (x, y)
2. Point 1 (-2, 5), Point 2 (3, -3), Midpoint (x, y)
3. Point 1 (2, 4), Point 2 (x, y), Midpoint (5, -1)
4. Point 1 (-1, 2), Point 2 (2, y), distance = 5
![Page 5: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/5.jpg)
ParallelogramsA parallelogram is a quadrilateral with both
pairs of opposite sides parallel
![Page 6: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/6.jpg)
Properties of ParallelogramsIts opposite sides are congruentIts opposite angles are congruentIts consecutive angles are supplementary
(add to 180°)Its diagonals bisect each other. (Cut each
other into 2 equal sections)
![Page 7: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/7.jpg)
Let’s PracticeFind the value of each variable in the
parallelogram.
![Page 8: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/8.jpg)
Let’s PracticeFind the value of each variable in the
parallelogram.
![Page 9: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/9.jpg)
Types of ParallelogramsRhombus – a parallelogram with four congruent
sides.Rectangle – a parallelogram with four right angles.Square – a parallelogram four congruent sides and
four right angles.Rhombus Corollary – a quadrilateral is a rhombus
if and only if it has four congruent sides.Rectangle Corollary – a quadrilateral is a
rectangle if and only if it has four right angles.Square Corollary – a quadrilateral is a square if
and only if it is a rhombus and a rectangle.
![Page 10: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/10.jpg)
Special Parallelogram PropertiesIf a parallelogram is a rhombus, its diagonals
are perpendicular.
If a parallelogram is a rhombus, each diagonal bisects a pair of opposite angles.
If a parallelogram is a rectangle, its diagonals are congruent.
![Page 11: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/11.jpg)
Let’s PracticeClassify the special quadrilateral. Explain
your reasoning. Then find the values of x and y.
![Page 12: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/12.jpg)
Let’s PracticeClassify the special quadrilateral. Explain
your reasoning. Then find the values of x and y.
![Page 13: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/13.jpg)
Other QuadrilateralsTrapezoid – a quadrilateral with exactly one
pair of parallel sides.
Kite – a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
![Page 14: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/14.jpg)
Trapezoid VocabularyBase - the parallel sides are the bases.Base Angles - in a trapezoid, the two angles
that have that base as a side.Legs – the non-parallel sides of a trapezoid.Isosceles Trapezoid – a trapezoid where
both legs are congruent.Midsegment of a Trapezoid – the segment
that connects the midpoints of the legs of a trapezoid.
![Page 15: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/15.jpg)
Trapezoid Properties For an isosceles trapezoid, each pair of base
angles is congruent.For an isosceles trapezoid, the diagonals are
congruent.Midsegment Theorem for Trapezoids –
the midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.
![Page 16: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/16.jpg)
Kite PropertiesIts diagonals are perpendicularExactly one pair of opposite angles are
congruent.The diagonal between the non-congruent
angles bisects the diagonal between the congruent angles.
![Page 17: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/17.jpg)
Let’s PracticeFind “x”.
![Page 18: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/18.jpg)
Let’s Practice
![Page 19: Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649ea95503460f94bae140/html5/thumbnails/19.jpg)
Let’s Practice