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Deck 5: Similar Triangles
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Question
Supply missing statements and missing reasons in the following proof.
Given:
in the figure shownProve:
S1. R1.S2.
R2.S3. R3. Vertical angles are congruent.
S4. R4.
Question
Where 
and 
are natural numbers and 
, let 
, 
, and 
.
Verify that
is a Pythagorean Triple.
and are natural numbers and , let , , and .Verify that
is a Pythagorean Triple. Question
Supply the missing reasons for the following proof.
Given:
and 
Prove: 
S1. 
and 
R1.S2.
R2.S3.
R3.S4.
R4.S5.
R5.S6.
R6. A property of proportionsS7.
R7. Substitution Property of Equality Question
Use the drawing provided to explain the 45
-45
-90
Theorem.
"In a triangle whose angles measure 45
, 45
, and 90
, the hypotenuse has a length equal to the product of
and the length of either leg."Given:
with 
, 
, and 
Prove: 
and 
Question
Explain (prove) the following property of proportions.
"If
(where 
and 
), then 
."
"If
(where and ), then ." Question
Supply missing statements and missing reasons for the following proof.
Given:
; 
bisects 
and 
Prove: 
is an isosceles triangleS1.
; 
bisects 
R1.S2.
R2. If a ray bisects one 
of a 
, it divides the oppositeside into segments whose lengths are proportional to
the lengths of the two sides that form the bisected
.S3. R3. Given
S4.
R4.S5.
, so 
R5.S6.
R6.S7. R7.
Question
Supply missing statements and missing reasons for the proof of this theorem.
"The altitude drawn to the hypotenuse of a right triangle separates the right triangle into two
right triangles that are similar to each other."
Given: Right triangle ABC with rt.
; 
Prove: 
S1. R1.S2.
R2.S3.
and 
are comp. R3. The acute angles of a rt. 
are comp.S4.
and 
are comp. R4.S5. R5. If 2
s are comp. to the same 
, these 
are 
.S6. R6.
Question
Provide the missing statements and missing reasons for the following proof.
Given:
and 
; 
and 
Prove: 
S1. R1. GivenS2.
R2.S3.
R3.S4. R4. CASTC
Question
Supply missing statements and missing reasons for the following proof.
Given:
; V is the midpoint of 
and W is the midpoint of 
.Prove:
S1. R1.S2.
and 
R2. Definition of midpointS3.
and 
R3.S4. R4. Substitution Property of Equality
S5.
R5.S6. R6.
Question
Provide all statements and all reasons for this proof.
Given:
with 
Prove: 
Question
Supply missing statements and missing reasons for for the following proof.
Given:
; 
and 
are right anglesProve:
S1. R1.S2.
R2.S3. R3.Opposite angles of a parallelogram.
S4.
R4.S5.
R5.S6. R6. In a proportion, the product of the means equals the
product of the extremes.
Question
Use the drawing(s) to explain the 30
-60
-90
Theorem.
"In a triangle whose angles measure 30
, 60
, and 90
, the hypotenuse has a length equal to twice the length of the shorter leg, and the length of the longer leg is the product of
andthe length of the shorter leg."
Given: Right
with 
, 
,and
; also, 
Prove: 
and 
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Deck 5: Similar Triangles
1
Supply missing statements and missing reasons in the following proof.
Given:
in the figure shownProve:
S1. R1.S2.
R2.S3. R3. Vertical angles are congruent.
S4. R4.
S1. 
in the figure shown
R1. Given
R2. If 2 parallel lines are cut by a trans, the alternate interior angles are congruent.
S3.
S4. 
R4. AA
in the figure shownR1. Given
R2. If 2 parallel lines are cut by a trans, the alternate interior angles are congruent.
S3.
S4. R4. AA 2
Where and are natural numbers and , let , , and .
Verify that is a Pythagorean Triple.
and are natural numbers and , let , , and .Verify that
is a Pythagorean Triple.We need to show that 
. Where 
, 
, and 
, it follws that 
or 
, so that 
, 
or 
, so that 
, and 
or 
, so that 
.
Now
or 
, which is the
value of
. That is, 
for all choices of 
and 
.
. Where , , and , it follws that or , so that , or , so that , and or , so that .Now
or , which is thevalue of
. That is, for all choices of and . 3
Supply the missing reasons for the following proof.
Given:
and Prove: S1. and R1.S2.
R2.S3.
R3.S4.
R4.S5.
R5.S6.
R6. A property of proportionsS7.
R7. Substitution Property of EqualityR1. Given
R2. Identity
R3. If 2 parallel lines are cut by a trans, corresponding angles are congruent.
R4. AA
R5. CSSTP
R2. Identity
R3. If 2 parallel lines are cut by a trans, corresponding angles are congruent.
R4. AA
R5. CSSTP
4
Use the drawing provided to explain the 45
-45
-90
Theorem.
"In a triangle whose angles measure 45
, 45
, and 90
, the hypotenuse has a length equal to the product of
and the length of either leg."Given:
with , , and Prove: and Unlock Deck
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5
Explain (prove) the following property of proportions.
"If (where and ), then ."
"If
(where and ), then ." Unlock Deck
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6
Supply missing statements and missing reasons for the following proof.
Given:
; bisects and Prove: is an isosceles triangleS1.
; bisects R1.S2.
R2. If a ray bisects one of a , it divides the oppositeside into segments whose lengths are proportional to
the lengths of the two sides that form the bisected
.S3. R3. Given
S4.
R4.S5.
, so R5.S6.
R6.S7. R7.
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7
Supply missing statements and missing reasons for the proof of this theorem.
"The altitude drawn to the hypotenuse of a right triangle separates the right triangle into two
right triangles that are similar to each other."
Given: Right triangle ABC with rt.
; Prove: S1. R1.S2.
R2.S3.
and are comp. R3. The acute angles of a rt. are comp.S4.
and are comp. R4.S5. R5. If 2
s are comp. to the same , these are .S6. R6.
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8
Provide the missing statements and missing reasons for the following proof.
Given:
and ; and Prove: S1. R1. GivenS2.
R2.S3.
R3.S4. R4. CASTC
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9
Supply missing statements and missing reasons for the following proof.
Given:
; V is the midpoint of and W is the midpoint of .Prove:
S1. R1.S2.
and R2. Definition of midpointS3.
and R3.S4. R4. Substitution Property of Equality
S5.
R5.S6. R6.
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10
Provide all statements and all reasons for this proof.
Given:
with Prove: Unlock Deck
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11
Supply missing statements and missing reasons for for the following proof.
Given:
; and are right anglesProve:
S1. R1.S2.
R2.S3. R3.Opposite angles of a parallelogram.
S4.
R4.S5.
R5.S6. R6. In a proportion, the product of the means equals the
product of the extremes.
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12
Use the drawing(s) to explain the 30
-60
-90
Theorem.
"In a triangle whose angles measure 30
, 60
, and 90
, the hypotenuse has a length equal to twice the length of the shorter leg, and the length of the longer leg is the product of
andthe length of the shorter leg."
Given: Right
with , ,and
; also, Prove: and Unlock Deck
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k this deck
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