Are you a rectangle?
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This document explores whether a quadrilateral defined by points A(0, -3), B(-4, 0), C(2, 8), and D(6, 5) is a rectangle. It finds that: 1) The lengths of opposite sides AB and CD are both 5 units and opposite sides BC and AD are both 10 units, showing the opposite sides are congruent. 2) The slopes of opposite sides AB and CD are both -3/4 and opposite sides BC and AD are both 4/3, showing the opposite sides are parallel. 3) The slopes of adjacent sides are negative reciprocals, showing the angles are right angles. Therefore, all properties of a rectangle are satisfied and
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Maths quadrilateral presentation
This document defines and provides properties of various quadrilaterals:
- A quadrilateral is a four-sided polygon with four interior angles summing to 360 degrees. Types include squares, rectangles, parallelograms, rhombuses, kites, and trapezoids.
- Rectangles have opposite parallel sides of equal length and right angles. The perimeter of a rectangle is the sum of its sides, and its area is length multiplied by width.
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- Rectangles have opposite parallel sides of equal length and right angles. The perimeter of a rectangle is the sum of its sides, and its area is length multiplied by width.
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479f3df10a8c0 mathsproject quadrilaterals
This document defines and describes different types of quadrilaterals. It begins by defining a quadrilateral as a polygon with four sides and four vertices. It then discusses the different taxonomic classifications of quadrilaterals, including parallelograms, trapezoids, kites, and more. Specific types of parallelograms like rectangles, rhombi, and squares are also defined. The document also proves various geometric properties of quadrilaterals, such as the angle sum property and the mid-point theorem.
Ch 6 quadrilaterals
This document provides information about polygons and quadrilaterals, including:
1) It defines different types of polygons based on their number of sides, such as triangles, quadrilaterals, pentagons, etc.
2) It covers properties and theorems about quadrilaterals such as the sum of interior angles of a quadrilateral equaling 360°, properties of parallelograms, and properties of special types of parallelograms like rectangles and squares.
3) It discusses trapezoids and kites, providing their definitions and properties like leg angles of trapezoids being supplementary and diagonals of kites bisecting opposite angles.
Math 8 – triangle congruence, postulates,
The document provides information about triangle congruence, including:
1. There are three postulates for proving triangles are congruent: side-side-side (SSS), side-angle-side (SAS), and angle-side-angle (ASA).
2. The SSS postulate states that if three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.
3. The SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.
4. The ASA postulate states that if two angles
Math 3.6
The document provides information about different types of quadrilaterals:
- Rhombus: all sides are equal length and opposite sides are parallel
- Square: four equal sides and four 90 degree angles
- Rectangle: all angles are 90 degrees, opposite sides are equal length and parallel
- Trapezoid: one pair of opposite sides are parallel
It describes teaching students to identify the properties of each quadrilateral type through group and independent work.
LET’S DO MATH.pptx
This document discusses geometry concepts like congruence, triangles, and their properties. It contains examples of:
- Using tangram pieces to complete a puzzle based on congruent shapes
- How congruence is used in mass production by ensuring identical copies are made
- Properties of triangle congruence like the reflexive, symmetric, and transitive properties
- Identifying sides, angles, and vertices of triangles in examples
- Defining terms and listing properties of congruence
The document provides instruction and activities to help students learn about geometric concepts like congruence through examples, definitions, and identifying parts of shapes.
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- 2. A Quadrilateral is located at A(0, -3), B(-4 0), C(2, 8) and D(6, 5). Is it a rectangle? Hmmmmmm...how do I begin? Remember, a rectangle has opposite sides that are parallel (same slope) and congruent, and four right angles (adjacent sides have negative reciprocal slopes). So, I need a plan… ★ Find the length of each side ★ Find the slope of each side and compare
- 3. Find each length... Use the distance formula from Lesson One - four times! ➔AB = 5 units (can you show me “how” this is true in an email?) ➔BC = 10 units ➔CD = 5 units ➔AD = 10 units Opposite sides are congruent! On to finding the slopes!
- 4. Find each slope… Remember, slope is (change in y)/(change in x) ➔AB = (0 - -3)/(-4 - 0) = -¾ ➔BC = (8 - 0)/(2 - -4) = 4/3 ➔CD = (5 - 8)/(6 - 2) = -¾ ➔AD = (5 - -3)/(6 - 0) = 4/3 Opposite sides have equal slopes so they are parallel! Adjacent sides have slopes that are negative reciprocals, so they are perpendicular!
- 5. Is the quadrilateral a rectangle? YES! Opposite sides are parallel and congruent, and because adjacent sides have negative reciprocal slopes, they are perpendicular and the quadrilateral has four right angles… In other words, rectangles are parallelograms with four right angles!