1.Find the distance between the two labeled points. (picture 1)A)2B)5 C)50D)252. What theorem can be used to prove that the two triangles are congruent?A) HL B) LA C) LL D) SSS
Accepted Solution
A:
Part (1):
The distance
between two points (x₁,y₁),(x₂,y₂) = d
[tex]d = \sqrt{ (x2-x1)^{2} + (y2-y1)^{2} } [/tex] The coordinates of the two labeled points are:(2,3) which are in the first quadrant(-3,-2) which are in the third quadrant∴ [tex]d = \sqrt{ (-3-2)^{2} + (-2-3)^{2} } [/tex] = 5√2
So, the distance between the two labeled points = 5√2 The correct answer is option B)5√2 =====================================================Part (2):Both of ΔABC and ΔDEF are right trianglesWe can conclude the following:1) ∠B = ∠E = 90°2) AC = DF ⇒⇒⇒ Hypotenuse 3) BC = EF ⇒⇒⇒ LegSo, the theorem that can be used to prove that the two triangles are congruent is HL