Quadrilaterals Worksheet With Answers Page 4
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50This theorem can be proven using the triangle congruence postulates and
theorems from the Congruent Triangles unit.
Given:
ABCD
D
C
AB ≅
Prove:
DC
AD ≅
BC
A
B
It is sometimes necessary to draw an auxiliary line such as the line containing
DB in the figure above. This auxiliary line can be drawn since two points
determine a line. Now it is possible to complete this proof.
Proof:
Statements
Reasons
1.
ABCD
1. Given
2. Draw auxiliary line DB
2. Two points determine a line.
3. Definition of a parallelogram
3. AB
DC and AD
BC
4. ∠ADB ≅ ∠CBD
4. If two parallel lines are cut by a
∠ABD ≅ ∠BDC
transversal, then the alternate
interior angles are congruent.
DB ≅
5.
DB
5. Reflexive property
6. ∆ ABD ≅ ∆ CDB
6. ASA congruence postulate
AD ≅
7. CPCTC
7.
BC
AB ≅
DC
2. Make a conjecture about the measures of the opposite angles of a
parallelogram.
Conjecture:___________________________________________________
Test this conjecture using the parallelogram in figure 3. First, Press F5 and
select Hide/show- objects. Hide the measures of the sides.
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