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At the right is a parallelogram ABCD.Consider each given information and answer the questions that follows.
1. a.If m∠d = 60°, find the m∠B._______
b.What property did you apply to determine the measurement of ∠B?_______________________________
2.a.If m∠A = 115°, find m∠D.__________
b.What property did you apply to determine the measure of ∠D?_________________________________
3.a.If ĀD = 9 cm,how long is BC?_______
b.What property did you apply to determine the measure of BC?_________________________________
4.If DĒ = 7 cm and ĀĒ = 6 cm, what is the length of DB =______and ĀC=_______?
5.Given: m∠ADC = 54° and m∠DCA =30°
a.What is the m∠DAC?________
b.What is the m∠ACB?________
c.What is the m∠BAC?________
d.What is the m∠ABC?________
e.What property did you apply to determine the measure of the angles?​

At The Right Is A Parallelogram ABCDConsider Each Given Information And Answer The Questions That Follows1 AIf Md 60 Find The MB BWhat Property Did You Apply To class=

Sagot :

Answer:

1. a. m∠D ≅ m∠B; therefore, m∠B = 60°

  b. Opposite angles in a parallelogram are congruent.

2. a. m∠D = 180 - m∠A = 180 - 115 = 65°

   b. Consecutive angles in a parallelogram are supplementary.

3. a. AD ≅ BC; therefore, BC = 9cm

   b. Opposite sides in a parallelogram are congruent.

4. a. [tex]DB=2DE=2(7)=14cm[/tex], [tex]AC=2AE=2(6)=12cm[/tex]

   b. Diagonals of a parallelogram bisect each other.

5. a. m∠DAC = 180 - m∠ADC - m∠DCA = 180 - 54 - 30 = 96°

   The sum of the interior angles of a triangle is 180°.

   b. m∠ACB = m∠DAC = 96°

   Alternate interior angles are congruent.

   c. m∠BAC = m∠DCA = 30°

   Alternate interior angles are congruent.

   d. m∠ABC = m∠ADC = 54°

   Opposite angles in a parallelogram are congruent.

   e. See the italicized statements

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