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Angle Pair Relationships Warmup Notes on Parallel Lines Parallel Lines Construction Activity

Angle Pair Relationships Warmup Notes on Parallel Lines Parallel Lines Construction Activity Parallel Lines and Transversals ( kuta ) Exit Quiz. Parallel lines – Two lines are parallel lines if they are coplanar and do not intersect.

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Angle Pair Relationships Warmup Notes on Parallel Lines Parallel Lines Construction Activity

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  1. Angle Pair Relationships Warmup Notes on Parallel Lines Parallel Lines Construction Activity Parallel Lines and Transversals (kuta) Exit Quiz

  2. Parallel lines – Two lines are parallel lines if they are coplanar and do not intersect. • Skew lines—Lines that do not intersect and are not coplanar. • Parallel planes—two planes that do not intersect.

  3. 1) Think of each segment in the diagram. Which appear to fit the description? Parallel to AB and contains D Perpendicular to AB and contains D. Skew to AB and contains D. Name the plane(s) that contains D and appear to be parallel to plane ABE B C D A F G E H

  4. If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. P l

  5. Exterior Angles Interior Angles Consecutive Interior Angles or Same Side Interior 1 2 3 4 Alternate Exterior Angles 6 5 8 7 Alternate Interior Angles Corresponding Angles

  6. 1. Using a straightedge, draw two nonparallel intersecting lines m and n. n A m 2. At point A, construct a line parallel to line m, by copying the angle formed by the intersection of lines m and n. n A m 3. Measure all eight angles formed by the parallel lines and transversal.

  7. 1 l m 2

  8. l m 1 2

  9. l m 1 2

  10. 1 l m 2

  11. If two lines are parallel to the same line, then they are parallel to each other. r q p If p║q and q║r, then p║r.

  12. b t 125° m a • 1. Find the measure of angle a and b if t // m. • Justify your reasoning using transformations. a = 125° by translating the given angle along the transversal b = 125° by rotating the given angle 180°

  13. 65° b t a m • 1. Find the measure of angle a and b if t // m. • Justify your reasoning using transformations. The given angle and b form a linear pair, therefore b = 115°. Rotate b 180° and translate along the transversal onto a. Therefore a = 115°

  14. Lines and Transversals Warmup Review of Parallel Lines Parallel Lines Quiz

  15. 2 1 4 3 l 6 5 8 7 m Correctly match the following and include the transformation that maps one angle onto its pair. • _________ 1. Alternate Interior Angles A. ∠4 and ∠6 E • Translate ∠3 along the transversal onto ∠7. Then rotate 180° onto ∠6 C _________ 2. Alternate Exterior Angles B. ∠1 and ∠ 5 ________ 3. Corresponding Angles C. ∠2 and ∠7 _________ 4. Consecutive Interior Angles D. ∠1 and ∠4 _________ 5. Vertical Angles E. ∠3 and ∠6 • Rotate ∠2 180° and then translate along the transversal onto ∠7 B • Translate ∠1 along the transversal onto ∠5 A • Not a transformation D Rotate ∠1180°

  16. Parallel Lines and Transversals Warmup Special Segments in Triangles Notes Segments in Triangles Worksheet Exit Quiz

  17. Objective: 1) Be able to identify the median of a triangle. 2) Be able to apply the Mid-segment Theorem. 3) Be able to use triangle measurements to find the longest and shortest side.

  18. B Midsegment E D A C

  19. Example B K J 6 L A C 10 1) Given: JK and KL are midsegments. Find JK and AB.

  20. Example 2) Find x.

  21. Median

  22. The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. If P is the centroid of ∆ABC, then AP = 2/3 AD, BP = 2/3 BF, and CP = 2/3 CE

  23. Exit Quiz: Special Segments in Triangles _____5. QT _____6. QR _____7.

  24. Rotations: Computers (Pullout) Special Segments in Triangles and Examining Midsegments Worksheets

  25. Algebra of Triangles Worksheet Warmup Quadrilateral Activity

  26. Quadrilateral Activity • Students will first cut out their set of triangles. • Mark the triangle on both sides if there are congruent sides or angles. • Using 2 or more triangles, they must transform the original triangles to form quadrilaterals • Then glue these quadrilaterals onto the butcher paper. • Next to the quadrilateral write down any characteristics that are displayed on the diagrams. • Present your findings.

  27. Quadrilateral Activity Notes on Quadrilaterals Who Want to Be a Quadrilateral Millionaire

  28. Objectives: • Be able to discover properties of quadrilaterals.

  29. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. REMEMBER, If two lines are parallel, then: P S 1) Alternate interior angles are congruent 2) Alternate exterior angles are congruent 3) Corresponding angles are congruent 4) Same-side interior angles are supplementary. Q R When you mark diagrams of quadrilaterals, use matching arrowheads to indicate which sides are parallel. For example, in the diagram above, PQ║RS and QR║SP. The symbol PQRS is read “parallelogram PQRS.”

  30. S P Q R S P R Q P S R Q S P M R Q

  31. 1) Find the value of each variable in the parallelogram below.

  32. W Z Y X

  33. Example: S P Q Q R

  34. Theorems about Parallelograms S P Q R S P R Q P S R Q S P R Q

  35. Theorems about Parallelograms S P Q R Summary

  36. Quadrilaterals A parallelogram with four congruent sides. Rhombus A parallelogram with four right angles. Rectangle A parallelogram with four congruent sides, and four right angles. Square

  37. 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. • You can use these to prove that a quadrilateral is a rhombus, rectangle or square without proving first that the quadrilateral is a parallelogram.

  38. 1) Decide whether the statement is always, sometimes, or never. A. A rectangle is a square. B. A square is a rhombus.

  39. A parallelogram is a rhombus if and only if its diagonals are perpendicular. Theorem 6.11 A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. Theorem 6.12 A parallelogram is a rectangle if and only if its diagonals are congruent. Theorem 6.13

  40. 2) Which of the following quadrilaterals have the given property? • All sides are congruent. • All angles are congruent. • The diagonals are congruent. • Opposite angles are congruent. • Parallelogram • Rectangle • Rhombus • Square

  41. 3) In the diagram at the right, PQRS is a rhombus. What is the value of y?

  42. Trapezoids A trapezoid is a quadrilateral with exactly one pair of parallel sides. Bases: The parallel sides of a trapezoid. Legs: The nonparallel sides of the trapezoid. Isosceles Trapezoid: A trapezoid whose legs are congruent. Midsegment: A segment that connects the midpoints of the legs and that is parallel to each base. Its length is one half the sum of the lengths of the bases. Base Midsegment Leg Leg Base Angles Base

  43. Isosceles Trapezoids A trapezoid that has congruent legs.

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