Subtraction Postulate 6. Subtraction Postulate
Subtraction Postulate 6. Subtraction Postulate
Subtraction Postulate 6. Subtraction Postulate
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Text p. 118 – 123<br />
Geometry<br />
Assignment #84<br />
Geometry Proof #3: <strong>Subtraction</strong> <strong>Postulate</strong><br />
<strong>6.</strong> <strong>Subtraction</strong> <strong>Postulate</strong>: If two sets of equal/congruent quantities are subtracted from each other,<br />
their differences are also equal/congruent.<br />
Given: AB = CD<br />
EF = GH<br />
Conclusion: AB – EF = CD – GH<br />
Reason: <strong>Subtraction</strong> <strong>Postulate</strong><br />
Directions: Given the following statements, solve each proof on a separate sheet of paper.<br />
1. Given: ∠ABC ≅ ∠DCB<br />
∠1 ≅ ∠2<br />
Prove: ∠3≅ ∠4<br />
2. Given: AD ≅ BC<br />
AE ≅ CF<br />
Prove: DE ≅ BF<br />
A<br />
M<br />
D<br />
D<br />
C<br />
3 1 2 4<br />
B<br />
C<br />
A<br />
E<br />
B<br />
F<br />
3. Given: DA ≅ CB<br />
DE ≅ CF<br />
Prove: EA ≅ FB<br />
4. Given: ∠WZY ≅∠ WXY<br />
∠RZY<br />
≅∠ RXS<br />
Prove: ∠WZR ≅∠ YXS<br />
D<br />
C<br />
Z<br />
S<br />
Y<br />
E<br />
F<br />
A<br />
B<br />
W<br />
R<br />
X
5. Given: FD ≅ GC<br />
FH ≅ GH<br />
E<br />
Prove: CH ≅ DH<br />
F<br />
G<br />
H<br />
C<br />
D<br />
R1. Point P is on line m. What is the total number of planes that are perpendicular to line m and<br />
pass through point P?<br />
(A) 1 (B) 2 (C) 0 (D) infinite<br />
R2. In the diagram of ΔABC below, AB ≅ AC. The measure of ∠ B is 40°.<br />
What is the measure of ∠A?<br />
R2<br />
R3<br />
R3. In the diagram above of parallelogram ABCD with diagonals AC and BD , m∠ 1=<br />
45 and<br />
m∠ DCB = 120. What is the measure of ∠ 2?<br />
R4. In the diagram, the length of the legs AC and BC of right<br />
ΔABC are 6 cm and 8 cm, respectively. Altitude CD is drawn<br />
to the hypotenuse of ΔABC. What is the length of AD to the<br />
nearest tenth of a meter?<br />
#1 – 5: Go over in class.<br />
R1. 1<br />
R2. 100<br />
R3. 15<br />
R4. 3.6
ANSWERS<br />
1. Statements Reasons<br />
1. ___________ Given<br />
2. ___________ Given<br />
3. ∠ABC −∠1 ≅ ∠DCB −∠2<br />
<strong>Subtraction</strong><br />
∠ABC ≅ ∠ 3 +∠1<br />
4.<br />
∠DBC ≅ ∠ 4 +∠2<br />
Partition<br />
5. ∠3≅ ∠4<br />
Substitution<br />
2. Statements Reasons<br />
1. ___________ Given<br />
2. ___________ Given<br />
3. AD −AE ≅BC − CF <strong>Subtraction</strong><br />
AD ≅ AE + ED<br />
4.<br />
BC ≅ CF + BF<br />
Partition<br />
5. DE ≅ BF<br />
Substitution<br />
3. Statements Reasons<br />
1. ___________ Given<br />
2. ___________ Given<br />
3. DA −DE ≅ CB − CF <strong>Subtraction</strong><br />
DA ≅ EA + DE<br />
4.<br />
CB ≅ FB + CF<br />
Partition<br />
5. EA ≅ FB<br />
Substitution<br />
4. Statements Reasons<br />
1. ___________ Given<br />
2. ___________ Given<br />
3.<br />
∠WZY −∠1 ≅∠WXY −∠ 2 <strong>Subtraction</strong><br />
∠WZY ≅∠ 1 +∠3<br />
4.<br />
∠WXY ≅∠ 2 +∠4<br />
Partition<br />
5. ∠3≅∠ 4<br />
Substitution<br />
5. Statements Reasons<br />
1. ___________ Given<br />
2. ___________ Given<br />
3. FD −FH ≅ GC − GH <strong>Subtraction</strong><br />
FD ≅ FH + DH<br />
4.<br />
GC ≅ GH + CH<br />
Partition<br />
5. CH ≅ DH<br />
Substitution<br />
R1. 1<br />
R2. 100<br />
R3. 15<br />
R4. 3.6
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