math key geometric ideas
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MATH Key Geometric Ideas. B. 45°. 45°. C. O. B. 90°. 90°. C. O. 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. 180°. 180°. B. C. O. - PowerPoint PPT PresentationTRANSCRIPT
MATHKey Geometric Ideas
B
OC
45°
45°
B
OC
90°
90°
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
C70°
70°
?
This rule goes both ways …
B
O
C
70°
70°
?
This rule goes both ways …
a b
180a b
B
O
C70°
70°110°
110°?
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.
B
O
C70°
70°110°
?
110 180x x
2 70x
35x
T
Q
PR
30°
?
S
T
Q
PR
30°
?
S
What fraction of the circle is shaded?
a
e
line 1
line 2
a eIf Line1 is parallel to Line2 , then:
ac
eg
line 1
line 2
180a c a e
180c e
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°
In quadrilateral PQRS below, sides PS and QR are parallel for what value of x ?
112°
x°P
S R
Q70°
In quadrilateral PQRS below, sides PS and QR are parallel for what value of x ?
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
A63° ?
B C D
E
+
147° 33
9057
33 90 180x
123 180x
57x
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 ?
ABCD is a trapezoid. What is angle BDC?
A
B C
D60°
30°
?°
line 1
line 2
65° 110°
x
Lines 1 and 2 are parallel. Find x.