- ABCD FGHJ. Find the measure of the given angles or lengths of the given sides. CD = 2x + 3; HJ = 3x + 2. Will all of the triangles be congruent?
these two are part of the same question please explain the answer.
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The problem does not provide as much information as the questions of problem need.
If the triangles the problem refers to are the triangles formed by diagonals of 4 sided polygons then you need to specify it, because there is an infinite number of possibilities of drawing triangles in the given 4 sided polygons.
Considering these triangles as those formed by diagonals, then they are congruent if only 4 sided polygons are congruent.
If all the lengths of each of 4 sided polygons are equal, then they are squares or rhombus.
You may find the lengths of each 4 sided polygons considering the congruence condition CD=HJ.
Substituting the equation 2x + 3 for CD and 3x + 2 for HJ yields:
2x + 3 = 3x + 2 => 2x - 3x = 2 - 3 => -x = -1 => x = 1
You need to substitute 1 for x in 2x + 3 and 3x + 2 such that:
CD = 2 + 3 = 5 units => by congruence yields that HJ = 5 units.
Hence, evaluating the lengths of CD and HJ yields that they measure 5 units each.
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