A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram: Side AB is parallel to side DC so t
he alternate interior angles, angle ABD and angle BDC, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by _______________. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which phrase best completes the student's proof?
2 answers:
Answer:
SAS rule
Step-by-step explanation:
To prove: A quadrilateral ABCD is a parallelogram.
Proof: It is given that ABCD is an equilateral, thus side AB is parallel to side DC so the alternate interior angles are congruent, thus ∠ABD and ∠BDC, are congruent.
Also, From ΔADB and ΔCDB, we have
AB=DC (Given)
∠ABD =∠BDC (Alternate angles)
DB=DB (Common)
Thus, by SAS rule of congruency, ΔADB is congruent to ΔCDB that is ΔADB≅ΔCDB.
By CPCTC, ∠DBC and ∠ADB are congruent and sides AD and BC are congruent. ∠DBC and ∠ADB form a pair of alternate interior angles.
Therefore, AD is congruent and parallel to BC.
Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.
Hence proved.
You might be interested in
Answer:
Each box of buns weighs 18 pounds and each box of potatoes weighs 35 pounds
Step-by-step explanation:
Let's say each bun box weighs b pounds and each potato box weighs p pounds. For each box of buns, we add b pounds. Therefore, for 40 boxes of buns, we add 40 * b pounds. Similarly, for 35 boxes of potatoes, we add 35 * p pounds.
For Tuesday, the total weight of the buns boxes is equal to 40 * b. The total weight of the potato boxes is equal to 35 * p. Adding these two together, we get the total weight of the boxes to be equal to
40 * b + 35 * p = 1945
For Friday, we can apply similar techniques to get
60 * b + 70 * p = 3530
We therefore have the two equations
40 * b + 35 * p = 1945
60 * b + 70 * p = 3530
One way to solve this would be to convert this into a matrix and use Guass-Jordan Elimination. With the amount of bun boxes representing the first column, the amount of potato boxes representing the second, and the total weight of each day representing the third, we have
One thing that we can do here is multiply the first row by -2 and add it to the second. That way, there would be a 0 in the 2nd column in the 2nd row, making an equation of the form
something * b = something else, enabling us to solve for b.
We thus have
Therefore, we can say that
-20 * b = -360
divide both sides by 20 to isolate b
b = 18
Therefore, each box of bunds weighs 18 pounds. Plugging that into an equation, we have
40 * b + 35 * p = 1945
40 * 18 + 35 * p = 1945
720 + 35 * p = 1945
subtract 720 from both sides to isolate the p and its coefficient
1225 = 35 * p
divide both sides by 35 to isolate p
p = 35
Therefore, each box of potatoes weighs 35 pounds
Answer:
Step-by-step explanation:
Given
Required
Determine the radius
Circumference (C) is calculated as:
Where r represents radius
Substitute values for C and
Multiply through by 7/44
<em>Hence, the radius is 35cm</em>
Answer:
500 lb
Step-by-step explanation:
Let x lb be the weight of seawater needed to get 17.5 lb of salt.
Now,
x lb - 100%
17.5 lb - 3.5%
Write a proportion:
Cross multiply: