Download Geometry Jeapordy

Classifying
Triangles
Proving
Congruence
Congruence
in Right
Triangles
Isosceles
Triangles
Coordinate
Proof
$100 $100 $100 $100 $100
$200 $200 $200 $200 $200
$300 $300 $300 $300 $300
$400 $400 $400 $400 $400
$500 $500 $500 $500 $500
Classifying Triangles for $100
Classify the following
triangle by sides and
angles. Give all possible
names:
Answer
Acute, equiangular,
equilateral, isosceles
Back
Classifying Triangles for $200
Define: Isosceles
Triangle
Answer
Isosceles Triangle – A three
sided polygon where two
or more sides are
congruent
Back
Classifying Triangles for $300
Classify the following
triangle by sides and
angles. Give all possible
names:
Answer
Isosceles, Right
Back
Classifying Triangles for $400
Classify the following
triangle by sides and
angles. Give all possible
names:
Answer
Scalene
Back
Classifying Triangles for $500
Given that the two triangles
below are congruent, then
triangle ABC is congruent to
_____. Also, identify the
congruent, corresponding
parts.
A
E
C
D
B
F
Answer
Triangle ABC is congruent to
Triangle EDF.
AB = ED
BC = DF
AC = EF
<A = <E
<B = <D
Back
<C = <F
Proving Congruence for $100
List all the ways to prove
congruence in right triangles:
Answer
HA – Hypotenuse- Angle
HL – Hypotenuse - Leg
LL – Leg - Leg
LA – Leg - Angle
Back
Proving Congruence for $200
List all the ways to prove
congruence in triangles:
Answer
ASA – Angle – Side – Angle
SAS – Side – Angle – Side
AAS – Angle – Angle – Side
SSS – Side – Side - Side
Back
Proving Congruence for $300
Given triangle ABC is
congruent to triangle PQR,
m<B = 3x+4, and m<Q = 8x-6,
find m<B and m<Q
Answer
m<B = m<Q => CPCTC
3x+4 = 8x – 6
10 = 5x
2=x
m<B = 3x+ 4 = 3*2+4 = 10 degrees
m<Q = 8x-6 = 8*2-6 = 10 degrees
Back
Proving Congruence for $400
Given: RS = UT; RT = US
Prove: Triangle RST = Triangle UTS
Answer
Statements
Reasons
RS = UT
Given
RT = US
Given
ST = ST
Reflexive Property of
Congruence
Triangle RST is
congruent to triangle
UTS
SSS
Back
Proving Congruence for $500
Can you prove that triangle FDG is
congruent to triangle FDE from the
given information? If so, how?
Answer
Yes, ASA or AAS
Back
Congruence in Right Triangles for
$100
Is it possible to prove that two of the
triangles in the figure below are
congruent? If so, name the right angle
congruence theorem that allows you to
do so.
Answer
Yes, Hypotenuse – Leg Congruence
Back
Congruence in Right Triangles for
$200
Given that AD is perpendicular to BC, name
the right angle congruence theorem that
allows you to IMMEDIATELY conclude that
triangle ABD is congruent to triangle ACD
Answer
Hypotenuse – Angle Congruence
Back
Congruence in Right Triangles for
$300
Name the right angle congruence
theorem that allows you to
conclude that triangle ABD is
congruent to triangle CBD
Answer
Leg- Leg Congruence
Back
Congruence in Right Triangles for
$400
Is there enough information to
prove that triangles ABC and
ADC are congruent? If so, name
the right angle congruence
theorem that allows you to do
so.
Answer
Yes, Hypotenuse – Leg Congruence
Back
Congruence in Right Triangles for
$500
What additional information will allow
you to prove the triangles
congruent by the HL Theorem?
Answer
AC is congruent to DC or
BC is congruent to EC
Back
Isosceles Triangles for $100
If a triangle is isosceles,
then the ___________
are congruent
Answer
If a triangle is isosceles,
then the base angles are
congruent
Back
Isosceles Triangles for $200
The angle formed by the
congruent sides of an
isosceles triangle is called
the ____________
Answer
The angle formed by the
congruent sides of an
isosceles triangle is called
the vertex angle
Back
Isosceles Triangles for $300
Name the congruent angles in
the triangle below. Justify
your answer:
B
A
C
Answer
<A  <C by the
Isosceles Triangle
Theorem
Back
Isosceles Triangles for $400
Given ABC is an equilateral triangle,
BD is the angle bisector of <ABC,
Prove that triangle ABD is a right
triangle
B
A
D
C
Answer
Statements
Reasons
AB = BC = AC
BD is the angle bisector of <ABC
Given
<ABD = <DBC
Definition of Angle bisector
<ABD = 60 degrees
Definition of a equilateral triangle
<ABD+<DBC = 60
Angle Sum Theorem
<ABD + <ABD = 60
Substitution
<ABD = 30
Simplify
<BAD = 60
Definition of a equilateral triangle
<BAD + <ADB + <ABD = 180 degrees
Triangle Sum Theorem
60 + 30 + <ADB = 180
Substitution
ADB = 90
Simplify
Triangle ABD is a right triangle
Definition of right triangles
Back
Isosceles Triangles for $500
Given ABC is an isosceles right
triangle, and BD is the angle
bisector of <ABC, Prove that
triangle ABD is isosceles
B
A
D
C
Answer
Statements
Reasons
AB = BC
ABC is a right triangle
BD is the angle bisector of <ABC
Given
<ABD = <DBC
Definition of Angle bisector
<ABD = 90 degrees
Definition of a right, isosceles triangle
<ABD+<DBC = 90
Angle Sum Theorem
<ABD + <ABD = 90
Substitution
<ABD = 45
Simplify
<BAC = <BCD
Isosceles Triangle Theorem
<BAC + <BCA + <ABC = 180 degrees
Triangle Sum Theorem
<BAC + <BAC + 90 = 180
Substitution
<BAC = 45
Simplify
<BAC = <ABD
Substitution
AD = BD
Isosceles Triangle Theorem
Triangle ABD is isosceles
Definition of Isosceles Triangles
Back
Coordinate Proof for $100
Draw the following triangle on
a coordinate plane. Label
the coordinates of the
vertices:
An equilateral triangle where
the length of the base is 2a
and the height is b
Answer
C (a,b)
A (0,0)
B (2a,0)
Back
Coordinate Proof for $200
Draw the following triangle
on a coordinate plane.
Label the coordinates of
the vertices:
A Scalene Triangle
Answer
C (b,c)
A (0,0)
B (a,0)
Back
Coordinate Proof for $300
Draw the following triangle
on a coordinate plane.
Label the coordinates of
the vertices:
An isosceles triangle with
base a and height c
Answer
C (a/2,c)
A (0,0)
B (a,0)
Back
Coordinate Proof for $400
Write a coordinate proof to prove
that if a line segment joins the
midpoints of two sides of a
triangle, then its length is equal to
one-half the length of the third
side.
Answer
ST = √(((a+b)/2) – (b/2))^2 + (c/2 – c/2)^2)
ST = √((a/2)^2 + 0)
ST = a/2
AB = √(((a-0)/2) – (b/2))^2 + (0 -0)^2)
AB = √((a)^2 + 0)
AB = a
C (b,c)
S (b/2,c/2)
T ((a+b)/2,c/2)
Thus, ST = ½ AB
A (0,0) B (a,0)
Back
Coordinate Proof for $500
Use coordinate proof to prove
that a triangle with base a
and height b such that the
vertex aligns vertically with
the midpoint of the base is
isosceles
Answer
CA = √((a/2 – 0)^2 + (b – 0)^2)
CA = √((a/2)^2 + b^2)
AB = √((a – a/2)^2 + (b -0)^2)
AB = √((a/2)^2 + b^2)
Thus CA = AB so Triangle ABC is Isosceles
C (a/2,b)
A (0,0) B (a,0)
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