Question

for each pair of triangles, tell which postulates, if any, make 1. △abc≅△efd 2. △ab 3. △abc≅△edf 4 5. △mad≅△mbc

Explanation:

Step1: Recall triangle - congruence postulates

The main triangle - congruence postulates are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze \(\triangle ABC\cong\triangle EFD\)

In \(\triangle ABC\) and \(\triangle EFD\), we have \(AB = EF\), \(BC=FD\), and \(AC = ED\). By the SSS postulate, if three sides of one triangle are equal to three sides of another triangle, the two triangles are congruent. So \(\triangle ABC\cong\triangle EFD\) by SSS.

Step3: Analyze \(\triangle ABC\cong\triangle EDF\)

We have \(AB = ED\), \(\angle A=\angle E\), and \(AC = EF\). By the SAS postulate (two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle), \(\triangle ABC\cong\triangle EDF\) by SAS.

Step4: Analyze \(\triangle MAD\cong\triangle MBC\)

We have right - triangles, \(MD = MC\) (hypotenuse) and \(MA=MB\) (leg). For right - triangles, by the HL (Hypotenuse - Leg) postulate, \(\triangle MAD\cong\triangle MBC\) by HL.

Answer:

1. SSS
2. SAS
3. HL