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Given: Kite KING Prove: Area of Kite KING =(KN)(IG)

Given: Kite KING Prove: Area of Kite KING =(KN)(IG)

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Activity: Use a two-column proof in proving the given 8. Area o theorem on kites below. Write your answer on a 2 separate sheet of paper. K Given: Kite KING Prove: Area of Kite KING = (KN)(IG)
Transcribed Image Text:Activity: Use a two-column proof in proving the given 8. Area o theorem on kites below. Write your answer on a 2 separate sheet of paper. K Given: Kite KING Prove: Area of Kite KING = (KN)(IG)
In a kite, diagonals are perpendicular. The area of a kite is half the product of the lengths of the diagonals. Given: Kite PRAY with PR = PY Prove: AP1 RY Given: Kite HOLY Prove: Area of kite HOLY = (HL)(OY) Statements 1. Kite PRAY with PR = Statements 1. Kite HOLY 2. HLLOY Reasons Reasons Given Given The diagonals of a kite PY and AR = AY are perpendicular to each 2. RJ = YJ If R and Y are equidistant from P and A, then J is equidistant from R and Y. SSS Triangle Congruence other. 3. Area of kite HOLY = Area of AOHL + Area Area Addition Postulate of ΔΗYL 3. ΔΡΙRΔΡΙΥ | 4. Area of AOHL = СРСТС 4. ZPJR = ZPJY 5. ZPJR and ZPJY form linear pair 6. ZPJR and ZPJY are (HL)(OB) Definition of linear pair Area formula for triangles Area of AHYL = (HL)(BY) 5. Area of kite HOLY= If two angles that form right angles a linear pair are (HL)(OB) + (HL)(BY) 6. Area of kite HOLY= (HL)(OB + BY) Substitution congruent, then each is a right angle. Definition of perpendicular (1) lines 7. AP1. RY Associative Property 7. OB + BY = OY Segment Addition Postulate Activity: Use a two-column proof in proving the given 8. Area of kite HOLY = theorem on kites below. Write your answer on a Substitution (HL)(OY) separate sheet of paper. Given: Kite KING Prove: Area of Kite KING = (KN)(IG)
Transcribed Image Text:In a kite, diagonals are perpendicular. The area of a kite is half the product of the lengths of the diagonals. Given: Kite PRAY with PR = PY Prove: AP1 RY Given: Kite HOLY Prove: Area of kite HOLY = (HL)(OY) Statements 1. Kite PRAY with PR = Statements 1. Kite HOLY 2. HLLOY Reasons Reasons Given Given The diagonals of a kite PY and AR = AY are perpendicular to each 2. RJ = YJ If R and Y are equidistant from P and A, then J is equidistant from R and Y. SSS Triangle Congruence other. 3. Area of kite HOLY = Area of AOHL + Area Area Addition Postulate of ΔΗYL 3. ΔΡΙRΔΡΙΥ | 4. Area of AOHL = СРСТС 4. ZPJR = ZPJY 5. ZPJR and ZPJY form linear pair 6. ZPJR and ZPJY are (HL)(OB) Definition of linear pair Area formula for triangles Area of AHYL = (HL)(BY) 5. Area of kite HOLY= If two angles that form right angles a linear pair are (HL)(OB) + (HL)(BY) 6. Area of kite HOLY= (HL)(OB + BY) Substitution congruent, then each is a right angle. Definition of perpendicular (1) lines 7. AP1. RY Associative Property 7. OB + BY = OY Segment Addition Postulate Activity: Use a two-column proof in proving the given 8. Area of kite HOLY = theorem on kites below. Write your answer on a Substitution (HL)(OY) separate sheet of paper. Given: Kite KING Prove: Area of Kite KING = (KN)(IG)
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