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shutvik [7]
3 years ago
7

State whether the triangles could be proven congruent, if possible, by SSS or SAS.

Mathematics
1 answer:
Helen [10]3 years ago
3 0

Answer:

1. SSS

2. SAS

3. SAS

4. SSS

5. SAS

6. SAS

Step-by-step explanation:

1) Side FY ≅ Side CW  Given

Side FP ≅ Side CM     Given

Side YP ≅ Side MW    Given

∴ΔMCW ≅ ΔFPY by the Side-Side-Side (SSS) rule of congruency

2) ∠CBD ≅ ∠BCA given that both are alternate interior angles

Side EB ≅ Side EC and Side DB ≅ Side CA Given

ΔBED ≅ ΔAEC by Side-Angle-Side (SAS) rule of congruency

3. ∠SVU ≅ ∠SVT   Given

Side SV ≅ Side SV  by reflexive property

Side VT ≅ Side VU   Given

∴ ΔVSU ≅ ΔVST by Side-Angle-Side (SAS) rule of congruency

4. Side MN ≅ Side QP  Given

Side MQ ≅ Side NP     Given

Side NQ ≅ Side NQ    by reflexive property

∴ΔQNM ≅ ΔQNP by the Side-Side-Side (SSS) rule of congruency

5. Indirect proof

Side GL ≅ Side HL  Given

Side GJ ≅ Side HK     Given

∠JLG ≅ ∠HLK    vertically opposite angles

By sine rule

GJ/sin(∠JLG) = GL/n(∠GJL)

Similarly

HK/sin(∠HLK) = HL/n(∠HKL)

∴ ∠GJL ≅ ∠HKL

∴ ∠LGJ ≅ ∠LHK third angle of two triangles given the other two angles are congruent

∴ΔQNM ≅ ΔQNP by the Side-Angle-Side (SAS) rule of congruency

6. ∠XZY ≅ ∠XZW   Supplementary ∠s with ∠XZY = 90°

Side XZ ≅ Side XZ  by reflexive property

Side ZW ≅ Side ZY   Given

∴ ΔXYZ ≅ ΔXWZ by Side-Angle-Side (SAS) rule of congruency.

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Step-by-step explanation:

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Reduce to simplest form. -\dfrac{1}{3}-\left(-\dfrac{3}{5}\right)=− 3 1 ​ −(− 5 3 ​ )=minus, start fraction, 1, divided by, 3, e
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Answer:

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Step-by-step explanation:

Reduce to simplest form

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What is the reciprocal of each mixed number? Drag and drop the answer into the box to match each number.
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Hi there!! 

First, we are going to find the improper fraction of each mixed number. 

10 1/3 >>>>> 10*3+1=31 31/3

2 2/3 >>>>> 2*3+2=8.      8/3 

5 1/3 >>>>>> 5*3+1 = 16.  16/3 

TO find the reciprocal, we switch the numerator with the denominator. 

31/3 changes to 3/31, 8/3 changes to 3/8, and finally 16/3 changes to 3/16. 


Your answer is: 

3/31
3/8
3/16

Hope this helps! Let me know if you have any questions:)
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3 years ago
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