Question

sides km and fh in the triangles below will be placed together to form a quadrilateral.
which best describes the quadrilateral that will be formed?
parallelogram
rectangle
rhombus
trapezoid

Explanation:

Analyze given triangles

We are given two triangles, \(\triangle MLK\) and \(\triangle FGH\). Let's list their known side lengths and angle measures:

• For \(\triangle MLK\): \(ML = 15\), \(LK = 35\), and the included angle \(\angle MLK = 110^\circ\).
• For \(\triangle FGH\): \(FG = 35\), \(GH = 15\), and the included angle \(\angle FGH = 110^\circ\).

Determine triangle congruence

Using the Triangle Congruence Theorems, specifically the Side-Angle-Side (SAS) postulate:

• \(ML = GH = 15\)
• \(\angle MLK = \angle HGF = 110^\circ\)
• \(LK = GF = 35\)

Therefore, \(\triangle MLK \cong \triangle HGF\). By Corresponding Parts of Congruent Triangles are Congruent (CPCTC), the third sides are equal:

$$KM = FH$$

Analyze the formed quadrilateral

The problem states that sides \(KM\) and \(FH\) are placed together to form a quadrilateral. Since \(KM = FH\), these two congruent sides will merge into a single diagonal inside the quadrilateral.
The outer boundary of the resulting quadrilateral will consist of the remaining four sides of the two triangles:

• Two sides of length \(15\) (\(ML\) and \(GH\))
• Two sides of length \(35\) (\(LK\) and \(FG\))

Since the triangles are congruent, they are joined along their corresponding congruent sides \(KM\) and \(FH\). This placement positions the opposite sides to be equal in length:

• One pair of opposite sides has length \(15\).
• The other pair of opposite sides has length \(35\).

Classify the quadrilateral

Using Quadrilateral Classification, a quadrilateral with two pairs of opposite sides that are equal in length is a parallelogram. Since the adjacent sides are unequal (\(15
eq 35\)) and the angles are not right angles, it is specifically a non-rectangular parallelogram.

Answer:

• parallelogram (Correct answer)
• rectangle
• rhombus
• trapezoid