7.4. Properties of Special Parallelograms For use with Exploration 7.4. Essential Question What are the properties of the diagonals of
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1 Name ate 7.4 Properties of Special Parallelograms For use with xploration 7.4 ssential Question What are the properties of the diagonals of rectangles, rhombuses, and squares? 1 XPLORTION: Identifying Special Quadrilaterals Go to igideasmath.com for an interactive tool to investigate this exploration. Work with a partner. Use dynamic geometry software. a. raw a circle with center. Sample b. raw two diameters of the circle. Label the endpoints,,, and. c. raw quadrilateral. d. Is a parallelogram? rectangle? rhombus? square? xplain your reasoning. e. Repeat parts (a) (d) for several other circles. Write a conjecture based on your results. 210 Geometry opyright ig Ideas Learning, LL ll rights reserved.
2 Name ate 7.4 Properties of Special Parallelograms (continued) 2 XPLORTION: Identifying Special Quadrilaterals Go to igideasmath.com for an interactive tool to investigate this exploration. Work with a partner. Use dynamic geometry software. a. onstruct two segments that are Sample perpendicular bisectors of each other. Label the endpoints,,, and. Label the intersection. b. raw quadrilateral. c. Is a parallelogram? rectangle? rhombus? square? xplain your reasoning. d. Repeat parts (a) (c) for several other segments. Write a conjecture based on your results. ommunicate Your nswer 3. What are the properties of the diagonals of rectangles, rhombuses, and squares? 4. Is RSTU a parallelogram? rectangle? rhombus? square? xplain your reasoning. R F S 5. What type of quadrilateral has congruent diagonals that bisect each other? U T opyright ig Ideas Learning, LL ll rights reserved. Geometry 211
3 Name ate 7.4 Notetaking with Vocabulary For use after Lesson 7.4 In your own words, write the meaning of each vocabulary term. rhombus rectangle square ore oncepts Rhombuses, Rectangles, and Squares rhombus is a rectangle is a square is a parallelogram parallelogram with parallelogram with with four congruent sides four congruent sides. four right angles. and four right angles. orollary 7.2 Rhombus orollary quadrilateral is a rhombus if and only if it has four congruent sides. is a rhombus if and only if. orollary 7.3 Rectangle orollary quadrilateral is a rectangle if and only if it has four right angles. is a rectangle if and only if,,, and are right angles. 212 Geometry opyright ig Ideas Learning, LL ll rights reserved.
4 Name ate 7.4 Notetaking with Vocabulary (continued) orollary 7.4 Square orollary quadrilateral is a square if and only if it is a rhombus and a rectangle. is a square if and only if and,,, and are right angles. Theorem 7.11 Rhombus iagonals Theorem parallelogram is a rhombus if and only if its diagonals are perpendicular. is a rhombus if and only if. Theorem 7.12 Rhombus Opposite ngles Theorem parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. is a rhombus if and only if bisects and. bisects and, and Theorem 7.13 Rectangle iagonals Theorem parallelogram is a rectangle if and only if its diagonals are congruent. is a rectangle if and only if. opyright ig Ideas Learning, LL ll rights reserved. Geometry 213
5 Name ate 7.4 Notetaking with Vocabulary (continued) xtra Practice 1. For any rhombus MNOP, decide whether the statement MO NP raw a diagram and explain your reasoning. is always or sometimes true. 2. For any rectangle PQRS, decide whether the statement PQS RSQ is always or sometimes true. raw a diagram and explain your reasoning. In xercises 3 5, the diagonals of rhombus intersect at. Given that m = 44, = 9, and = 7, find the indicated measure m 7 44 In xercises 6 8, the diagonals of rectangle FGH intersect at I. Given that m HFG = 31 and G = 17, find the indicated measure. F 6. m FHG 7. HF 8. m FH 31 I In xercises 9 11, the diagonals of square LMNP intersect at K. Given that 1 MK =, find the indicated measure. L 2 9. PK 10. m PKN 11. m MNK H G 1 2 M K P N 214 Geometry opyright ig Ideas Learning, LL ll rights reserved.
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Math 3 - Lesson Title: Using the Coordinate Plane for Proofs
Targeted Content Standard(s): Use coordinates to prove simple geometric theorems algebraically. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove
Polygon Interior Angles
Polygons can be named by the number of sides. A regular polygon has All other polygons are irregular. A concave polygon has All other polygons are convex, with all vertices facing outwards. Name each polygon
An angle that has a measure less than a right angle.
Unit 1 Study Strategies: Two-Dimensional Figures Lesson Vocab Word Definition Example Formed by two rays or line segments that have the same 1 Angle endpoint. The shared endpoint is called the vertex.