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- 2. Quadrilateral – is a four-sided polygon.
- 3. NAMING a QUADRILATERAL and the PARTS of it • Quadrilateral Name • Sides • Angles • Diagonals • Consecutive Angles • Consecutive Sides • Opposite Angles • Opposite Sides
- 4. NAMING a QUADRILATERAL and the PARTS of it • Quadrilateral Name • Sides • Angles • Diagonals • Consecutive Angles • Consecutive Sides • Opposite Angles • Opposite Sides
- 5. QUADRILATERALS : FAMILY TREE
- 6. QUADRILATERALS : FAMILY TREE KITE – is a quadrilateral with two distinct pairs of consecutive sides that are congruent
- 7. QUADRILATERALS : FAMILY TREE TRAPEZOID – is a quadrilateral with only one pair of parallel opposite sides
- 8. QUADRILATERALS : FAMILY TREE PARALLELOGRAM – is a quadrilateral with only two pairs of parallel opposite sides
- 9. QUADRILATERALS : FAMILY TREE RHOMBUS – is a parallelogram with four congruent sides
- 10. QUADRILATERALS : FAMILY TREE RECTANGLE – is a parallelogram with four right angles
- 11. QUADRILATERALS : FAMILY TREE SQUARE – is a parallelogram that has four congruent sides and four right angles
- 12. QUADRILATERALS : FAMILY TREE 1. A rectangle is a parallelogram. 2. A square is a rhombus. 3. A square is a parallelogram. 4. A square is a quadrilateral. 5. A rhombus is a square. 6. A rectangle is a square. 7. A trapezoid is a quadrilateral. 8. A kite is a trapezoid. 9. A square is a rectangle. 10. A trapezoid is a parallelogram.
- 13. PARALLELOGRAM A parallelogram is a quadrilateral that has two pairs of opposite sides that are parallel. PROPERTIES: 1. Opposite sides are congruent (≅). 2. Opposite angles are congruent. 3. Consecutive angles are supplementary. 4. Diagonals bisect each other.
- 14. RHOMBUS A rhombus is a parallelogram that has four congruent sides. PROPERTIES: 1. All properties inherited from the parallelogram. 2. Diagonals are perpendicular (⊥). 3. Each diagonal bisects the angles of a rhombus.
- 15. RECTANGLE A rectangle is a parallelogram that has four right angles. PROPERTIES: 1. All properties inherited from the parallelogram. 2. Diagonals are congruent.
- 16. SQUARE A square is a parallelogram that has four congruent sides and four right angles. PROPERTIES: 1. All properties inherited from the parallelogram. 2. All properties of rhombus. 3. All properties of a rectangle
- 17. Example: A. Find the measures of the indicated parts of parallelogram ABCD with diagonals intersecting at point O using the properties of a parallelogram. 1. AB = 2. BC = 3. OC = 4. DO = 5. 𝒎∠𝑫𝑨𝑩 = 6. 𝒎∠ABC = 7. Perimeter of parallelogram ABCD =
Hinweis der Redaktion
- SIDES: ABCD is a quadrilateral with four sides namely 𝑨𝑩̅̅̅̅, 𝑩𝑪̅̅̅̅, 𝑪𝑫̅̅̅̅ and 𝑫𝑨̅̅̅̅. It has four vertices A, B, C and D. In naming a quadrilateral you may start at any vertex and move with the next vertex clockwise or counterclockwise. ANGLES: The angle between two adjacent sides is an angle of the quadrilateral. So, a quadrilateral has four angles that is, ∠DAB or ∠A, ∠ABC or ∠B, ∠BCD or ∠C and ∠CDA and ∠D. Note: You may name an angle using a single letter/vertex if one angle shares that vertex. A line segment joining a pair of opposite vertices is called a diagonal. So, there are two diagonals namely 𝑨𝑪̅̅̅̅ and 𝑩𝑫̅̅̅̅̅.
- QUADRILATERAL NAME MNOP, NOPM, OPMN, PMNO, MPON, NMPO, ONMP, PONM SIDES 𝑴𝑵̅̅̅̅̅, 𝑵𝑶̅̅̅̅̅, 𝑴𝑷̅̅̅̅̅, 𝑷𝑶̅̅̅ ANGLES ∠𝑴, ∠𝑵, ∠𝑶, ∠𝑷 DIAGONALS 𝑴𝑶̅̅̅̅̅, 𝑵𝑷̅̅̅̅̅ Pairs of Consecutive Sides 𝑴𝑵̅̅̅̅̅ and 𝑵𝑶̅̅̅̅̅ 𝑵𝑶̅̅̅̅̅ and 𝑷𝑶̅̅̅̅ 𝑷𝑶̅̅̅̅ and 𝑴𝑷̅̅̅̅̅ 𝑴𝑷̅̅̅̅̅ and 𝑴𝑵̅̅̅̅̅ Pairs of Opposite Sides 𝑴𝑵̅̅̅̅̅ and 𝑷𝑶̅̅̅̅ 𝑵𝑶̅̅̅̅̅ and 𝑴𝑷̅̅̅̅ Pairs of Consecutive Angles ∠𝑴 and ∠𝑵 ∠𝑵 and ∠𝑶 ∠𝑶 and ∠𝑷 ∠𝑷 and ∠𝑴 Pairs of Opposite Angles ∠𝑴 and ∠𝑶 ∠𝑵 and ∠𝑷
- 1. 𝑨𝑩=? Answer: 𝑨𝑩=𝟑𝟑, opposite sides are of a parallelogram are congruent, 𝑨𝑩̅̅̅̅ is the opposite side of 𝑫𝑪̅̅̅̅. 2. 𝑩𝑪=? Answer: 𝑨𝑩=𝟏𝟎, opposite sides are of a parallelogram are congruent, 𝑩𝑪̅̅̅̅ is the opposite side of 𝑨𝑫̅̅̅̅. 3. 𝑶𝑪=? Answer: 𝑶𝑪=𝟗, diagonals of a parallelogram bisect each other, 𝑨𝑶̅̅̅̅≅𝑶𝑪̅̅̅̅. 4. 𝑫𝑶=? Answer: 𝑫𝑶=𝟏𝟏, diagonals of a parallelogram bisect each other, 𝑫𝑶 is half the measurement of 𝑩𝑫. 5. 𝒎∠𝑫𝑨𝑩=? Answer: 𝒎∠𝑫𝑨𝑩=𝟏𝟎𝟖°, opposite angles are congruent, ∠𝑩𝑪𝑫≅∠𝑫𝑨𝑩. 6. 𝒎∠𝑨𝑩𝑪=? Answer: 𝒎∠𝑨𝑩𝑪=𝟕𝟐°, consecutive angles are supplementary, the sum of 𝒎∠𝑩𝑪𝑫 and 𝒎∠𝑨𝑩𝑪 is 𝟏𝟖𝟎°. 7. Perimeter of parallelogram ABCD = ? Answer: Perimeter of parallelogram ABCD =𝟔𝟒, perimeter is the sum of all sides, 32+10+32+10=64.