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Dec 17, 2015
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Classifying Triangles
Proving Congruence
Coordinate Proof
Congruence in Right Triangles
Isosceles Triangles
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
Back
Scalene
Classifying Triangles for $500Given that the two triangles below
are congruent, then triangle ABC is congruent to _____. Also, identify the congruent, corresponding parts.
A
B
C
D
E
F
Triangle ABC is congruent to Triangle EDF.AB = EDBC = DFAC = EF<A = <E<B = <D<C = <F
Answer
Back
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 => CPCTC3x+4 = 8x – 610 = 5x2 = xm<B = 3x+ 4 = 3*2+4 = 10 degreesm<Q = 8x-6 = 8*2-6 = 10 degrees
Back
Proving Congruence for $400
Given: RS = UT; RT = US
Prove: Triangle RST = Triangle UTS
Answer
Back
Statements ReasonsRS = UT Given
RT = US Given
ST = ST Reflexive Property of Congruence
Triangle RST is congruent to triangle UTS
SSS
Proving Congruence for $500
Can you prove that triangle FDG is congruent to triangle FDE from the given information? If so, how?
Answer
Back
Yes, ASA or AAS
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
Back
Yes, Hypotenuse – Leg Congruence
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
Back
Hypotenuse – Angle Congruence
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
Back
If a triangle is isosceles, then the base angles are congruent
Isosceles Triangles for $200
The angle formed by the congruent sides of an isosceles triangle is called the ____________
Answer
Back
The angle formed by the congruent sides of an isosceles triangle is called the vertex angle
Isosceles Triangles for $300
Name the congruent angles in the triangle below. Justify your answer:
A
B
C
Answer
Back
<A <C by the Isosceles Triangle Theorem
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
A
B
CD
Answer
Back
Statements ReasonsAB = 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
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
A
B
CD
Answer
Back
Statements ReasonsAB = BCABC 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
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
Back
A (0,0) B (2a,0)
C (a,b)
Coordinate Proof for $200
Draw the following triangle on a coordinate plane. Label the coordinates of the vertices:
A Scalene Triangle
Answer
Back
A (0,0) B (a,0)
C (b,c)
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
Back
A (0,0) B (a,0)
C (a/2,c)
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
BackA (0,0) B (a,0)
C (b,c)
S (b/2,c/2) T ((a+b)/2,c/2)
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
Thus, ST = ½ AB
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
BackA (0,0) B (a,0)
C (a/2,b)
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
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