Your line 4 should have "angle DEC" not "angle EDC". The order of the letters is important. I marked the two angles ABC and DEC in the attached image below. They are alternate interior angles. Because DE || AB, this means the alternate interior angles are congruent.
Since C is the midpoint of EB, this means BC = CE by the definition of the midpoint. Basically EB is cut into two halfs BC and CE which are the same length.
After you establish all of what is mentioned previously, you would use the AAS congruence theorem. AAS stands for Angle Angle Side. One pair of angles are the vertical angles (see line 2). Another pair of congruent angles is the alternate interior angles (line 4). The sides are not between the pairs of angles mentioned. Again check out the attached image for more visual information.
Finally, if we know the triangles are congruent, then the corresponding parts are congruent (CPCTC). That leads to the conclusion that DC = AC.
Edit: it's actually ASA and not AAS because the sides are between the two angles (I was thinking of another diagram earlier)
Answer:
A=4.
Step-by-step explanation:
Note: In the expression of area the first term should be .
It is given that area of a rectangular floor of your house is and the length is
units.
We know that, area of a rectangle is
Since length of the rectangle is , therefore
is a factor of
and the value of
is 0 at x=-2.
Divide both sides by 4.
Therefore, the value of A is 4.
Answer:
105°, 75°, and 105°.
Step-by-step explanation:
If two straight paths intersect at a point , four angles will be formed.
These are pairs of vertical angles.
The adjacent angles add up to 180°
If one of the angles is 75°, the supplement will be
Therefore the three other angles will be , 105°, 75°, and 105°.
Answer:
16 faults
Step-by-step explanation:
<u><em>The correct question is</em></u>
In tennis, a first serve can be an ace, a fault, or it can be returned. In one match, a tennis player hit 24 aces, which was 2/5 of all her first serves. If 1/3 of her first serves were returned, how many of the tennis player's first serves were faults?
Let
x -----> the number of all her first servers
y ----> the number of first services returned
z ---> the number of first services faults
we know that
The number of aces plus the number of returned plus the number of faults must be equal to the number of all her first services
so
step 1
Find out the number of all her first servers
we have that
Solve for x
step 2
Find out the number of first services returned
substitute the value of x
step 3
Find out the number of first services faults
we have
substitute and solve for z