Suppose that J is between H and K. If HJ=2x+4, JK=3x+3, and KH=22, find the lengths of HJ and JK. Remember to always draw an image first and to pay attention to what the question is asking for! Find the Segment Addition Postulate Use the Segment Addition Postulate and then substitute what we know. Do not use any spaces in your answers.

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Ответ:

greenhappypiggies

08.03.2021

Mathematics

A) ΔGCB ≅ ΔERG

B) Angle-Angle (AA) Similarity Theorem

C) BE = 266 2/3 PE = 233 1/3

Step-by-step explanation:

GC || ER therefore, by Alternate Interior Angles Theorem: ∠G ≡ ∠E

GR || CE therefore, by Alternate Interior Angles Theorem: ∠C ≡ ∠R

Since we have two congruent angles, we can prove ΔGCB and ΔERG are congruent using the Angle-Angle (AA) Similarity Theorem.

Since it is a parallelogram, the sides are congruent (GC = RP and GR = CP)

GC = 350 GB = 400 CB = 300

ER = 350 + PE EG = 400 + BE RG = 300 + 200

Since the triangles are similar, their sides are proportional.

$\dfrac{GC}{ER}=\dfrac{GB}{EG}=\dfrac{CB}{RG}$

$\dfrac{GC}{ER}=\dfrac{CB}{RG} \quad \implies \quad \dfrac{350}{350+PE}=\dfrac{300}{300+200}\\\\\\.\qquad \qquad \qquad \qquad \qquad 350(500)=300(350+PE)\\\\\\.\qquad \qquad \qquad \qquad \qquad 175,000=105,000+300PE\\\\\\.\qquad \qquad \qquad \qquad \qquad 70,000=300PE\\\\\\.\qquad \qquad \qquad \qquad \qquad \dfrac{70,000}{300}=PE\\\\\\.\qquad \qquad \qquad \qquad \qquad \dfrac{700}{3}=PE\\\\\\.\qquad \qquad \qquad \qquad \qquad \large\boxed{233\dfrac{1}{3} =PE}$

$\dfrac{GB}{EG}=\dfrac{CB}{RG} \quad \implies \quad \dfrac{400}{400+BE}=\dfrac{300}{300+200}\\\\\\.\qquad \qquad \qquad \qquad \qquad 400(500)=300(400+BE)\\\\\\.\qquad \qquad \qquad \qquad \qquad 200,000=120,000+300BE\\\\\\.\qquad \qquad \qquad \qquad \qquad 80,000=300BE\\\\\\.\qquad \qquad \qquad \qquad \qquad \dfrac{80,000}{300}=BE\\\\\\.\qquad \qquad \qquad \qquad \qquad \dfrac{800}{3}=BE\\\\\\.\qquad \qquad \qquad \qquad \qquad \large\boxed{266 \dfrac{2}{3}=BE}$

The diagram below models the layout at a carnival where G, R, P, C, B, and E are various locations o

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