1. Rotate ABC 180° about the origin making DEF. List all congruent sides and angles:
1 answer:
Answer:
<h3> ∠ABC≅∠DEF </h3><h3> ∠BCA≅∠EFD </h3><h3> ∠CAB≅∠FDE </h3><h3> AB≅DE, BC≅EF, CA≅FD</h3>Step-by-step explanation:
To rotate point A 180° about the origin (point O) we draw a line from that point (A) throu the origin, measure the distance from the point A to the origin, and then measure the same distance on the other side of the origin to get rotated point. Mark it. The angle at the rotated point will be congruent to ∠A
The same goes for points B and C
Angles at pair of given and rotated point are congruent.
Sides of triangle are congruent if they lay between two congruent angles.
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, we have the quadratic formula
,
where a is the coefficient (number before the variable) of the squared term, b is the coefficient of the linear term, and c is the constant term.
So, given
, we can get that 
, and 
. We substitute these numbers into the quadratic formula above.
This is our final answer.
If you've never seen the quadratic formula, you can derive it by completing the square for the general form of a quadratic. Note that the
symbol (read: plus or minus) represents the two possible distinct solutions, except for zero under the radical, which gives only one solution.
where a is the coefficient (number before the variable) of the squared term, b is the coefficient of the linear term, and c is the constant term.
So, given
This is our final answer.
If you've never seen the quadratic formula, you can derive it by completing the square for the general form of a quadratic. Note that the