Mathematics: Geometry ! complete the following proof. given: qk=16, pk=26, mk=65, kl=40 prove: ∆qpk~∆lmk

35 is the rangStep-by-step explanation:...

Geometry ! complete the following proof. given: qk=16,

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trent1002brown

09.03.2022

Mathematics

Statement 2.: QK/KL=16/40; PK/MK=26/65

Statement 3.: QK/KL=2/5=PK/MK

Reason 4: Vertical angles

Reason 5: SAS

Step-by-step explanation:

Statement 2:

The smaller of the sides adjacent to <PKQ (QK=16) in triangle PKQ is corresponding with the smaller of the sides adjacent to <MKL (KL=40) in triangle MKL.

The larger of the sides adjacent to <PKQ (PK=26) in triangle PKQ is corresponding with the larger of the sides adjacent to <MKL (MK=65) in triangle MKL.

Ratio of the corresponding sides:

$\frac{QK}{KL}=\frac{16}{40}$

$\frac{PK}{MK}=\frac{26}{65}$

Statement 3. Simplifying ratios:

Dividing the numerator and denominator by 8:

$\frac{QK}{KL}=\frac{\frac{16}{8}}{\frac{40}{8}}\\ \frac{QK}{KL}=\frac{2}{5}$

Dividing the numerator and denominator by 13:

$\frac{PK}{MK}=\frac{\frac{26}{13}}{\frac{65}{13}}\\ \frac{PK}{MK}=\frac{2}{5}$

Reason 4: <MKL is conguent with <PKQ because they are vertical angles (angles opposite by the vertex)

Reason 5: The two triangles (∆QPK y ∆LMK) have a congruent angle (<MKL with <PKQ) and the corresponding sides including this angle proportionals (QK/KL=2/5=PK/MK), then the two triangles (∆QPK y ∆LMK) are similar. This case is SAS.

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Geometry ! complete the following proof. given: qk=16, pk=26, mk=65, kl=40 prove: ∆qpk~∆lmk

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