Given: Quadrilateral DEFG is a parallelogram.
22
What is the reason for step 5 in this proof
OA Vertical Angles Theorem
OB. Opposite interior angles of a parallelogram are congruer
OC All angles of a rectangle have the same measure
OD. Alternate Interior Angles Theorem
G
Prove GHE EM
DHE FH
2. DE|GP
lare
Proof
Statement
Reason
1. Quadrilateral DEFG is a parallelogram. given
DGBP
definition of a parallelogram
3. Draw DP and GE . These line segments
cransversals cutting two pairs of parallel lines: drawing line segments
DE and GP and DG and EP.
4. Place point Hwhere DP and GE intersect. defining a point
5. LHGD HEF
HDGA ZHFE
Opposite sides of a
6. DG EF
parallelogram are congruent.
7.
ASA criterion for congruence
B. GHE SH
Corresponding sides of
congruent triangles are
DHE FH
congruent

Answer: Opposite interior angles of a parallelogram are congruent.

Explanation:

It is given that  DEFG is a parallelogram.

Draw the diagonals DF and EG. Place point H where DF and EG intersect.

In triangle HGD and HEF,

∠HGD ≅ ∠HEF                            (Alternate Interior angle)

∠HDG ≅ ∠HFE                      (Alternate Interior angle)

By the definition of a parallelogram, the opposite sides of a parallelogram are congruent.

DG ≅ EF                                      (Opposite sides of parallelogram)

According to ASA postulate, two triangles are congruent if any two angles and their included side are equal in both triangles.

So, by using ASA criterion for congruence we get,

ΔDGH ≅ ΔFEH

Since corresponding sides of congruent triangles are congruent, therefore

GH ≅ EH                      (CPCTC)

DH ≅ FH                     (CPCTC)

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two sets of parallel sides. Both the congruence of opposite sides and the congruence of opposite angles require the Euclidean parallel postulate, or one of its equivalent formulations, and neither condition can be proved without it.

The values of the three supplied variables x, y, and z in the parallelogram are given to us.

Let's abbreviate the parallelogram, which is depicted in the attached image, ABCD.

Here,

m∠CAB = 31°,  m∠ABC =96°.

Since CD and AB are parallel, AC is a transversal now. So,

m∠CAB =m∠ACD

m∠ACD=31°

x=31

From the ΔABC we have,

m∠ABC +m∠ACB+m∠BAC=180°

96°+Y+31°=180°

y+127°=180°

y=153°

y=153

And also we know that the measure of opposite angles in a parallelogram are always equal.

So, m∠ADC=m∠ABC

z=96°

z=96

Therefore, the required values of x, y, z are 31, 153, 96.

To know more about parallelogram, visit:

brainly.com/question/19187448

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The web page you created displays the time in the correct time zone for the user's location.


What language was most likely to have been used?

C. JavaScript
Because -- If a web page displays the current time, the web page probably uses JavaScript to make it happen

In a black box experiment, when the amount of material exiting a closed system is less than the amount of material entering the system, what conclusion can the experimenter make?
A.
that material remained in the system
B.
that material was lost
C.
that it will be difficult to make an accurate measurement
D.
that parts of the system need to change