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PLEASE HELP!!!

Angle CAE is congruent to angle___

Angle CBF is congruent to angle___

PLEASE HELP!!! Angle CAE is congruent to angle___ Angle CBF is congruent to angle-example-1
User Pierre Baret
by
2.7k points

1 Answer

17 votes
17 votes

Answer:

Angle CAE is congruent to angle CBE

Angle CBF is congruent to angle CAF

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Step-by-step explanation:

Angle CAE is an inscribed angle that subtends the minor arc CE

Minor arc CE is the distance around the circle from C to E following the shorter path. All minor arcs are smaller than 180 degrees.

What other inscribed angle also subtends minor arc CE? That would be inscribed angle CBE

Notice that CAE and CBE both have "C" and "E" as the first and last items. The only change is the middle letter. This is a quick nonvisual way to determine inscribed angles.

Recall that if two inscribed angles subtend the same arc, then they are congruent. Therefore, angle CAE is congruent to angle CBE

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For similar reasoning, angles CBF and CAF are congruent inscribed angles that subtend minor arc CF.

For more information, check out the inscribed angle theorem. Also I recommend using GeoGebra as a handy tool.

User EKons
by
2.4k points
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