Question

in the figure below, $\triangle ijk \cong \triangle lmn$.

(there is a figure of two triangles: $\triangle ijk$ (blue) and $\triangle lmn$ (yellow). in $\triangle lmn$, side $ln = 8.06$, side $lm = 6.04$, side $mn = 8.32$, angle $\angle n = 43^\circ$, angle $\angle m = 66^\circ$.)

which of the following statements is true?

a. $m\angle kij = 71^\circ$

b. $jk = 6.04$

c. $m\angle ikj = 66^\circ$

d. $ij = 8.06$

Explanation:

Step1: Recall Triangle Congruence

Since \(\triangle IJK \cong \triangle LMN\), corresponding angles and sides are equal. First, find the missing angle in \(\triangle LMN\). The sum of angles in a triangle is \(180^\circ\). So, \(m\angle L = 180^\circ - 43^\circ - 66^\circ = 71^\circ\).

Step2: Match Corresponding Parts

• Corresponding angles: \(\angle KIJ\) corresponds to \(\angle L\), so \(m\angle KIJ = 71^\circ\) (matches option A).
• Check other options:
• \(JK\) corresponds to \(MN\) (length 8.32), so B is wrong.
• \(m\angle IKJ\) corresponds to \(m\angle MNL = 43^\circ\), so C is wrong.
• \(IJ\) corresponds to \(LM\) (length 6.04), so D is wrong.

Answer:

A. \(m\angle KIJ = 71^\circ\)