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Geometry
Notes 6.9
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Name:_______________________________________
Period:____
I can use the distance formula and slope formula to prove or disprove a figure is s type of quadrilateral. G.GPE.4
Error Analysis
Find the error(s) if any in each of the following examples. Be able to explain how to fix it or how you would have solved
the problem correctly.
Example One-
Example Two-
Example ThreeA Pizza Hut building is made up of several isosceles trapezoids. Prove that base angles of the roof are congruent.
Statements
Reasons
1) PIZA is an isosceles trapezoid
1) Given
2) Draw in 𝑃𝑍 and 𝐴𝐼
2) Any two points determine a line segment
3) 𝑃𝑍 ≅ 𝐴𝐼
4) ∠𝐼𝐴𝑍 ≅ ∠𝑃𝑍𝐴
3) The diagonals of an isosceles trapezoid are congruent.
4) If lines are parallel, then alternate interior angles are congruent.
5) 𝐴𝑍 ≅ 𝐴𝑍
6) ∆𝑃𝑍𝐴 ≅ ∆𝐼𝐴𝑍
7) ∠𝑃𝐴𝑍 ≅ ∠𝐼𝑍𝐴 (bases angles)
5) Reflexive
6) SAS
7) CPCTC
Example Four-
A
The kite at right is a mathematically correct kite. Explain in sentences using words
that the diagonals meet at right angles.
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By definition, a kite has adjacent sides congruent so ̅̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐴𝐷 . By the reflexive
property ̅̅̅̅̅
𝐴𝑀 ≅ ̅̅̅̅̅
𝐴𝑀. By HL, ∆𝐴𝑀𝐷 ≅ ∆𝐴𝑀𝐵 which means the diagonals of the
kite must meet at right angles.
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B
Geometry
Homework 6.9
Name:________________________________________
Period:____
Algebra Find the value(s) of the variable(s) in each isosceles trapezoid.
7.
8.
9.
Find the measures of the numbered angles in each kite.
10.
11.
13.
14.
Over
12.
Find the measure of the numbered angles for each parallelogram.
1.
2.
3.
4. What is the precise name of a quadrilateral with vertices
?
Find the values of the variables for which each figure is a parallelogram.
5.
6.
Find the values of the variables.
1.
2.
3.
In Exercises 4 and 5, decide whether the statement is true or false. If true, explain why. If false, show a
counterexample.
4. A quadrilateral with congruent and perpendicular diagonals is a square or rhombus.
5. The diagonals of a kite separate the quadrilateral into four congruent triangles.