Geometry Quiz

Quiz by Maladroit
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Last updated: May 18, 2018
First submittedMay 18, 2018
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8-1
If the altitude is drawn
to the hypotenuse of a
right triangle, then the two
triangles formed are
similar to the original
triangle and to each other.
 
8-1 (C1)
When the altitude is drawn
to the hypotenuse of a
right triangle, the
length of the altitude is the
geometric mean between
the segments of the hypotenuse.
 
8-1 (C2)
When the altitude is drawn
to the hypotenuse of a
right triangle, each leg is the
geometric mean between the
hypotenuse and the segment of
the hypotenuse that is
adjacent to that leg.
 
8-2
In a right triangle, the
square of the hypotenuse is
equal to the sum of the
squares of the legs.
 
8-3
If the square of one side of
a triangle is equal to the sum of
the squares of the other two
sides, then the triangle is a
right triangle.
 
8-6
In a 45-45-90 triangle,
the hypotenuse is √2 times as
long as a leg.
 
8-7
In a 30-60-90 triangle,
the hypotenuse is twice as long
as the shorter leg, and the
longer leg is √3 times as long as
the shorter leg.
 
9-1
If a line is tangent to a
circle, then the line is
perpendicular to the
radius drawn to the
point of tangency.
 
9-1 (C1)
Tangents to a circle from
a point are congruent.
9-2
If a line in the plane of a
circle is perpendicular to a
radius at its outer
endpoint, then the line is
tangent to the circle.
 
P16
The measure of the arc formed
by two adjacent arcs is the
sum of the measures of
these two arcs.
(Arc Addition Postulate.)
 
9-3
In the same circle or in
congruent circles, two
minor arcs are congruent if
and only if their central angles
are congruent.
 
9-4
In the same circle or in
congruent circles:
(1) Congruent arcs have
congruent chords.
(2) Congruent chords have
congruent arcs.
 
9-5
A diameter that is
perpendicular to a chord
bisects the chord and its arc.
 
9-6
In the same circle or in
congruent circles:
(1) Chords equally distant from the
centre (or centres) are congruent.
(2) Congruent chords are equally
distant from the centre (or centres).
 
9-7
The measure of an inscribed
angle is equal to half the measure
of its intercepted arc.
 
9-7 (C1)
If two inscribed angles intercept
the same arc, then the angles
are congruent.
9-7 (C2)
An angle inscribed in a
semicircle is a right angle.
 
9-7 (C3)
If a quadrilateral is
inscribed in a circle, then its
opposite angles are
supplementary.
 
9-8
The measure of an angle
formed by a chord and a tangent
is equal to half the measure
of the intercepted arc.
 
9-9
The measure of an angle
formed by two chords that intersect
inside a circle is equal to half
the sum of the measures of
the intercepted arcs.
 
9-10
The measure of an angle formed
by two secants,
two tangents,
or a secant
and a tangent
drawn from a point outside a circle
is equal to half the difference
of the measures of
the intercepted arcs.
 
9-11
When two chords intersect inside
a circle, the product of the
segments of one chord equals
the product of the segments of
the other chord.
 
9-12
When two secant segments are
drawn to a circle from an external
point, the product of one secant
segment and its external segment
equals the product of the other
secant segment and its
external segment.
 
9-13
When a secant segment and
a tangent segment are drawn to
a circle from an external point,
the product of the
secant segment and its
external segment is equal to
the square of the
tangent segment.
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