In ΔABC, m∠ACB = 90°, CD ⊥ AB and m∠ACD = 45°. Find: AC, if CD = 6√2 in.
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Answer:
The answer to your question is: (4, -1)
Step-by-step explanation:
M = midpoint (-1, 1)
A = (-6, 3)
B = (x, y)
x = 2xm - x1
x = 2(-1) + 6
x = -2 + 6
x = 4
y = 2ym - y1
y = 2(1) - 3
y = 2 - 3
y = -1
There are several ways two triangles can be congruent.
<em> congruent by SAS</em>
<em> congruent by corresponding theorem</em>
In and
(see attachment), we have the following observations
--- Because O is the midpoint of line segment AD
--- Because O is the midpoint of line segment BC
---- Because vertical angles are congruent
---- Because vertical angles are congruent
Using the SAS (<em>side-angle-side</em>) postulate, we have:
Using corresponding theorem,
---- i.e. both triangles are congruent
The above congruence equation is true because:
- <em>2 sides of both triangles are congruent</em>
- <em>1 angle each of both triangles is equal</em>
- <em>Corresponding angles are equal</em>
See attachment
Read more about congruence triangles at:
