GEOMETRY PROOFS!
1 answer:
From the given figure ,
RECA is a quadrilateral
RC divides it into two parts
From the triangles , ∆REC and ∆RAC
RE = RA (Given)
angle CRE = angle CRA (Given)
RC = RC (Common side)
Therefore, ∆REC is Congruent to ∆RAC
∆REC =~ ∆RAC by SAS Property
⇛CE = CA (Congruent parts in a congruent triangles)
Hence , Proved
<em>Additional comment:-</em>
SAS property:-
"The two sides and included angle of one triangle are equal to the two sides and included angle then the two triangles are Congruent and this property is called SAS Property (Side -Angle-Side)
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Applying the required <em>rule </em>or <em>theorem</em>, it can be concluded that the second biker is <u>farther</u> from the <em>parking lot</em>. The distance of the bikers to the <em>parking lot</em> are:
i. First biker = 17.0 km
ii. Second biker = 20.22 km
The <u>path</u> of travel of both bikers would form a triangle. Applying the <u>Pythagoras</u> theorem to the path of the <em>first</em> biker would give his <u>distance</u> from the starting point. While applying the <u>cosine</u> rule to the path of <em>second</em> rider would gives his <u>distance</u> to the starting point.
Thus,
a. <u>To determine the distance of the first biker from the parking lot.</u>
Let the required <em>distance </em>be represented by x. Applying the Pythagoras theorem, we have:
=
+
=
+
= 64 + 225
= 289
x =
= 17
x = 17 km
Thus, the <u>first</u> biker is 17.0 km from the <em>starting</em> point.
b. <u>To determine the distance of the second biker from the parking lot.</u>
Let the required <em>distance</em> be represented by x. So that applying the cosine rule, we have:
=
+
- 2ab Cos θ
=
+
- 2(15*8) Cos (180 - 20)
= 64 + 225 - 240 Cos 160
= 289 - 240 * -0.5
= 289 + 120
= 409
x =
= 20.2237
x = 20.22 km
Thus, the <u>second</u> biker is 20.22 km from the <em>starting</em> point.
Therefore, the second biker is <u>farther</u> from the <em>parking lot</em>.
A sketch of the path of travel for the two bikers is attached for more clarifications.
Visit: brainly.com/question/22699651
Answer:
Step-by-step explanation:
Given equation :
Making the terms of 'x' to one side and constants to the other.
So, the value of 'x' is 29.