Question

lesson 9: side-side-side triangle congruence
cool down: practice seeing shortcuts
label each example by whether you could prove the triangles congruent using:

• side-side-side triangle congruence theorem
• side-angle-side triangle congruence theorem
• angle-side-angle triangle congruence theorem
• none of the above

1. triangle abd is congruent to triangle acd.
2. triangle ejh is congruent to triangle eih.
3. triangle lkn is congruent to triangle mkn.

Explanation:

1. Triangle \(ABD\) and \(ACD\)

Step1: Analyze sides

In a circle, \(AB = AC\) (radii of the same circle). \(AD\) is common to both triangles \(ABD\) and \(ACD\). But we don't know if \(BD=CD\). Also, we don't have information about included angles.

Step2: Check congruence theorems

Since we can't confirm \(SSS\) (don't know \(BD = CD\)), \(SAS\) (no included - angle info), or \(ASA\) (no angle - side - angle info), we use the non - congruence option.

2. Triangle \(EJH\) and \(EIH\)

Step1: Identify right angles

\(\angle EJH=\angle EIH = 90^{\circ}\). \(JH = IH\) (given as equal segments) and \(EH\) is common.

Step2: Apply \(SAS\)

The side \(EH\) is common, the right angles (\(\angle EJH\) and \(\angle EIH\)) are equal, and \(JH = IH\). So, by the \(SAS\) (Side - Angle - Side) congruence theorem, \(\triangle EJH\cong\triangle EIH\).

3. Triangle \(LKN\) and \(MKN\)

Step1: Analyze sides and angles

\(LK = MK\) (radii of the same circle), \(KN\) is common. But we don't know if \(\angle LKN=\angle MKN\).

Step2: Check congruence theorems

Since we can't confirm \(SSS\) (no info on \(LN = MN\)), \(SAS\) (no included - angle info), or \(ASA\) (no angle - side - angle info), we use the non - congruence option.

Answer:

1. None of the above
2. Side - Angle - Side Triangle Congruence Theorem
3. None of the above