Question: User: Formative Assessment
Statement
HJ \cong MJ
KJ \cong LJ
Reason
Given
m\angle H = 50^\circ
m\angle K = 70^\circ
Reason
Given
m\angle HJK = 60^\circ
Reason
Interior Sum Theorem
m\angle HJK = m\angle MJL
= 60^\circ
Reason
Vertical Angles
\triangle HJK \cong \triangle MJL
Reason
SAS
m\angle K = m\angle L
= 60^\circ
Reason
Corresponding Parts of Congruent Triangles
A. Vertical Angles
B. Alternate Interior Angles
C. Reflexive Property
D. Alternate Exterior Angles
graph shapes and math: A coordinate-plane graph in the top-left shows points H, K, J, L, and M connected by two intersecting line segments forming triangles HJK and MJL, with angle marks labeled 50^\circ near H and 70^\circ near K; position_hint = top-left
1. **State the problem:** We are given two triangles \(\triangle HJK\) and \(\triangle MJL\) with certain congruent sides and angles, and we need to identify which reason corresponds to the statement about vertical angles.
2. **Given:**
- \(HJ \cong MJ\)
- \(KJ \cong LJ\)
- \(m\angle H = 50^\circ\)
- \(m\angle K = 70^\circ\)
- \(m\angle HJK = 60^\circ\)
3. **Interior Sum Theorem:** The sum of interior angles in a triangle is \(180^\circ\). This confirms \(m\angle HJK = 60^\circ\).
4. **Vertical Angles:** The angles \(\angle HJK\) and \(\angle MJL\) are vertical angles formed by intersecting lines, so \(m\angle HJK = m\angle MJL = 60^\circ\).
5. **Triangle Congruence:** Using Side-Angle-Side (SAS) postulate, \(\triangle HJK \cong \triangle MJL\) because two sides and the included angle are congruent.
6. **Corresponding Parts:** From congruent triangles, corresponding angles \(\angle K\) and \(\angle L\) are congruent, so \(m\angle K = m\angle L = 60^\circ\).
7. **Answer:** The reason that corresponds to the equality of \(m\angle HJK\) and \(m\angle MJL\) is **A. Vertical Angles**.
**Final answer:** A. Vertical Angles