Which of the following statements are true based on the diagram?

Mathematics

1 answer:

WINSTONCH [101]4 years ago

5 0

Its true yo 1234567891011121314

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Solve the system of equations 2r - 6y= 28 -x-y = 14 PLEASE HELP

o-na [289]

Answer:

$\displaystyle [-7, -7]$

Step-by-step explanation:

{2x - 6y = 28

{−x - y = 14

−⅙[2x - 6y = 28]

{−⅓x + y = −4⅔

{−x - y = 14

____________

$\displaystyle \frac{-1\frac{1}{3}x}{-1\frac{1}{3}} = \frac{9\frac{1}{3}}{-1\frac{1}{3}} \\ \\$

$x = -7$ [Plug this back into both equations above to get the y-coordinate of −7]; $\displaystyle -7 = y$

I am joyous to assist you anytime.

3 0

4 years ago

Han wrote a proof that triangle BCD is congruent to triangle DAB. Han's proof is incomplete. Which step is missing some informat

Ede4ka [16]

Answer:

The answer is below

Step-by-step explanation:

From the image, we can see that DC is parallel to AB.

Step 1:

Alternate interior angles are angles formed at the inner corners of intersection on opposite sides of transversal when two parallel lines are intersected by a transversal.

Since Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.

Step 2:

DB ≅ BD (reflexive property of congruence)

Step 3:

∠A = ∠C = 90° (right angles, given). But to prove that both triangles are congruent, the correct step 3 is:

Since, ∠A = ∠C = 90° and angles CDB and ABD are congruent. This means that the third angles in the both triangles are also congruent. Hence, angle ADB and CBD are must be congruent.

Step 4:

BD = DB, angles CDB and ABD are congruent, angle ADB and CBD are congruent.

Therefore, By the Angle-Side-Angle Triangle Congruence Theorem, triangle BCD is congruent to triangle DAB .