Which statement can be used to prove that the two triangles are congruent?

Mathematics

2 answers:

prohojiy [21]2 years ago

8 0

Answer:

HL Theorem

Step-by-step explanation:

Here, we see that both triangles have a right angle, making them right triangles. We know that the hypotenuse must be equivalent, as it is the same line. Furthermore, we see that one of the legs from each triangle are equivalent. Therefore, we can use HL Theorem to prove these triangles are equal.

slamgirl [31]2 years ago

5 0

Answer:

The SAS postulate

Step-by-step explanation:

Longer lengths of the two triangles are equal (S)

The triangles are reflected about the line where their equal hyputenuses meet (S)
The right angle of one triengle is equal to the right angle of the other triengle (A)

Thus the two triangles are congruent as evidenced by the SAS postulate.

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A segment with endpoints A (2, 1) and C (4, 7) is partitioned by a point B such that AB and BC form a 3:2 ratio. Find B.

sdas [7]

$\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(2,1)\qquad C(4,7)\qquad \qquad \stackrel{\textit{ratio from A to C}}{3:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{3}{2}\implies \cfrac{A}{C} = \cfrac{3}{2}\implies 2A=3C\implies 2(2,1)=3(4,7)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill$

$\bf B=\left(\cfrac{(2\cdot 2)+(3\cdot 4)}{3+2}\quad ,\quad \cfrac{(2\cdot 1)+(3\cdot 7)}{3+2}\right)\implies B=\left( \cfrac{4+12}{5}~,~\cfrac{2+21}{5} \right) \\\\\\ B=\left(\cfrac{16}{5}~~,~~\cfrac{23}{5} \right)\implies B=\left( 3\frac{1}{5}~~,~~4\frac{3}{5} \right)$