MATH Key Geometric Ideas. B O C 45° B O C 90° B O C 180° There is a direct relationship between...
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Transcript of MATH Key Geometric Ideas. B O C 45° B O C 90° B O C 180° There is a direct relationship between...
BO
C
180°
180°
There is a direct relationship between the central angle and the arc subtended by that
central angle.
Even if you don’t remember the rule, you can tell the rule just by looking at simple
examples.
B
O
C
These are both the same length, because they’re both radii of the circle.
Now form a triangle.
If sides of a triangle are equal lengths, then the opposite angles are equal.
112°
x°P
S R
Q70°
In quadrilateral PQRS below, sides PS and QR are parallel for what value of x ?
Mark the parallel lines. This is the first – and most important – step.
To make clear where the parallel lines are cut by a diagonal line, extend them.
112°
x°P
S R
Q70° 70°
In quadrilateral PQRS below, sides PS and QR are parallel for what value of x ?
110x
In the figure below, A, B, C, and D are collinear, FC is parallel to ED, BE is
perpendicular to ED, and the measures of FAB and EBA are as marked. What is the
measure of FCB ?
A63° 147° ?
B C D
E
+
In the figure below, A, B, C, and D are collinear, FC is parallel to ED, BE is
perpendicular to ED, and the measures of FAB and EBA are as marked. What is the
measure of FCB ?
A63° ?
B C D
E
+
147° 33
9057
47. In the figure below, AB || CD, AE bisects ∠BAC, and CE bisects ∠ACD. If the measure of ∠BAC is 82°, what is the measure of ∠AEC ?
47. In the figure below, AB || CD, AE bisects ∠BAC, and CE bisects ∠ACD. If the measure of ∠BAC is 82°, what is the measure of ∠AEC ?