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The document discusses different types of quadrilaterals: - Parallelograms have both pairs of opposite sides parallel. - Rhombuses have four equal sides. - Rectangles have four right angles. - Squares are both rhombuses and rectangles, with four equal sides and four right angles. Theorems state that a quadrilateral is a rhombus if its diagonals are perpendicular, or if each diagonal bisects a pair of opposite sides. A quadrilateral is a rectangle if its diagonals are parallel.
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8.4 notes
1) A quadrilateral is a parallelogram if its diagonals bisect each other and both pairs of opposite sides are congruent.
2) For a quadrilateral to be a parallelogram, x must be such that the opposite sides are parallel.
3) Theorems are presented about the properties of rhombuses, rectangles, and squares as special types of parallelograms.
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8.4 notes
1. A quadrilateral is a parallelogram if both pairs of opposite sides are parallel and equal in length.
2. The diagonals of a parallelogram bisect each other.
3. For a quadrilateral to be a parallelogram, the value of x must make both pairs of opposite sides parallel and equal in length.
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- Examples are provided for classifying quadrilaterals and finding unknown angle measures using the fact that the sum of interior angles in any quadrilateral is always 360 degrees.
- Students are assigned homework problems involving classifying triangles and quadrilaterals and finding unknown angle measures.
Obj. 27 Special Parallelograms
Prove and apply properties of rectangles, rhombuses, and squares.
Use properties of rectangles, rhombuses, and squares to solve problems.
Prove that a given quadrilateral is a rectangle, rhombus, or square.
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This document discusses different types of quadrilaterals including their definitions and properties. It defines a quadrilateral as a four-sided polygon and introduces various terms used to describe quadrilateral parts such as sides, angles, and diagonals. It then presents different types of quadrilaterals in a family tree showing their relationships and provides detailed definitions and properties for parallelograms, rhombuses, rectangles, and squares. The document concludes with an example problem involving finding measurements of a parallelogram using its properties.
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8.4 notes
1) A quadrilateral is a parallelogram if its diagonals bisect each other and both pairs of opposite sides are congruent.
2) For a quadrilateral to be a parallelogram, x must be such that the opposite sides are parallel.
3) Theorems are presented about the properties of rhombuses, rectangles, and squares as special types of parallelograms.
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This document defines various math vocabulary terms from A to Z. It provides short, one sentence definitions for terms like arithmetic, bisect, circumference, decagon, exponents, fractions, graphs, hexagon, increase, jump discontinuity, kappa, least common multiple, multiplication, numbers, octagon, parallel, quotient, radius, second, ten, unit, volume, weight, x, y-axis, and zero. The document is intended to familiarize the reader with basic math terminology.
8.4 notes
1. A quadrilateral is a parallelogram if both pairs of opposite sides are parallel and equal in length.
2. The diagonals of a parallelogram bisect each other.
3. For a quadrilateral to be a parallelogram, the value of x must make both pairs of opposite sides parallel and equal in length.
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This document provides a course description, rationale, materials, and expectations for a 10th grade geometry class. The course will cover traditional geometry topics through transformations, symmetry, graph theory, and coordinate and synthetic geometry. Students will develop logical thinking skills. The textbook is Geometry by McDougal & Littell and additional online resources will be used. The teacher's contact information is provided. Students are expected to follow class rules, complete daily bellwork and homework, and will be assessed through quizzes, tests, and projects. Grades are calculated based on a percentage point system.
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- The document discusses classifying triangles and quadrilaterals based on their side lengths and angles. It defines different types of quadrilaterals such as parallelograms, rectangles, rhombuses, trapezoids, and squares.
- Examples are provided for classifying quadrilaterals and finding unknown angle measures using the fact that the sum of interior angles in any quadrilateral is always 360 degrees.
- Students are assigned homework problems involving classifying triangles and quadrilaterals and finding unknown angle measures.
Obj. 27 Special Parallelograms
Prove and apply properties of rectangles, rhombuses, and squares.
Use properties of rectangles, rhombuses, and squares to solve problems.
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This document discusses different types of quadrilaterals including their definitions and properties. It defines a quadrilateral as a four-sided polygon and introduces various terms used to describe quadrilateral parts such as sides, angles, and diagonals. It then presents different types of quadrilaterals in a family tree showing their relationships and provides detailed definitions and properties for parallelograms, rhombuses, rectangles, and squares. The document concludes with an example problem involving finding measurements of a parallelogram using its properties.
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8.4 notes
This document discusses different types of quadrilaterals:
- Parallelograms have both pairs of opposite sides parallel.
- Rhombuses have four equal sides.
- Rectangles have four right angles.
- Squares are both rhombuses and rectangles, with four equal sides and four right angles.
Theorems are presented about the properties of rhombuses, rectangles, and relationships between diagonals and the shape of the quadrilateral. Examples are given of proving properties of rhombuses using definitions and properties of parallel lines. Homework problems are assigned.
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8.4 notes
- 2. 8.4 Special Quadrilaterals January 27, 2014 8.4 Special Quadrilaterals Rectangle: w/ 4 right <s Rhombus: w/ 4 ≅ sides Square: w/ 4 sides ≅ & 4 right <s Rhombus Corollary: A quad is a rhombus iff it has 4 ≅ sides. Rectangle Corollary: A quad is a rectangle iff it has 4 right <s. Square Corollary: A quad is a square iff it is a rhombus and rectangle. Parallelograms Rhombuses Rectangles Squares Dec 2212:19 PM HW pg. 537 #351 multiples of 3 2
- 6. 8.4 Special Quadrilaterals January 27, 2014 Rewrite the theorem as a biconditional and prove it. Theorem 8.11 A is a rhombus iff its diagonals are . Conditional Statement If the diagonals of a are , then it is a rhombus. Converse If the is a rhombus, then its diagonals are . PROOF: Questions to ask. What do I know about //ograms? What do I know about rhombuses? Given: ABCD is a ; AC BD Prove: ABCD is a rhombus. A B X D Statements 1. ABCD is a //ogram 2. AC BD 3. <CXB & <DXC are right <s 4. <CXB ≅ <DXC 5. AD ≅ BC & DC ≅ AB 6. DX ≅ BX 7. CX ≅ XC 8. BXC ≅ DXC 9. BC ≅ DC 10. AD DC & BC AB ≅ ≅ 11. ABCD is a rhombus C Reasons 1. Given 2. Given 3. Def of lines 4. Def of right <s 5. Opp. sides of are ≅ 6. Diagonals bisect each other in 7. Reflexive Prop. 8. SAS 9. CPCTC 10. Transitive Prop. 11. Def of rhombus Jan 39:08 AM HW pg. 537 #351 multiples of 3 6