Question

triangle congruence
triangle congruence worksheet #1
for each pair of triangles, tell which postulates, if any, make the triangles congruent.

1. ( \triangle abc cong \triangle efd )
2. ( \triangle abc cong \triangle cda )
3. ( \triangle abc cong \triangle efd )
4. ( \triangle adc cong \triangle bdc )
5. ( \triangle mad cong \triangle mbc )

( \triangle abe cong \triangle cde )

1. ( \triangle acb cong \triangle adb )
2. ( \triangle mnp cong \triangle mqp )

Explanation:

12.

Step1: Identify corresponding sides

In \(\triangle ABC\) and \(\triangle EFD\), we have \(AB = ED\), \(AC = EF\), \(BC = FD\).

Step2: Apply congruence postulate

By the Side - Side - Side (SSS) congruence postulate, if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

13.

Step1: Identify corresponding sides

In \(\triangle ABC\) and \(\triangle CDA\), \(AB = CD\), \(BC = DA\), \(AC=CA\) (common side).

Step2: Apply congruence postulate

By the Side - Side - Side (SSS) congruence postulate.

14.

Step1: Identify side - angle - side

In \(\triangle ABC\) and \(\triangle EFD\), \(AB = ED\), \(\angle A=\angle E\), \(AC = EF\).

Step2: Apply congruence postulate

By the Side - Angle - Side (SAS) congruence postulate.

15.

Step1: Identify right angles and sides

In \(\triangle ADC\) and \(\triangle BDC\), \(\angle ADC=\angle BDC = 90^{\circ}\), \(AC = BC\), \(CD = CD\) (common side).

Step2: Apply congruence postulate

By the Hypotenuse - Leg (HL) congruence postulate (for right - angled triangles).

21.

Step1: Identify right angles and sides

In \(\triangle MAD\) and \(\triangle MBC\), \(\angle A=\angle B = 90^{\circ}\), \(MD = MC\), \(MA = MB\).

Step2: Apply congruence postulate

By the Hypotenuse - Leg (HL) congruence postulate.

22.

Step1: Identify vertical angles and sides

\(\angle AEB=\angle DEC\) (vertical angles), \(AE = CE\), \(BE = DE\).

Step2: Apply congruence postulate

By the Side - Angle - Side (SAS) congruence postulate.

23.

Step1: Identify sides and angle

In \(\triangle ACB\) and \(\triangle ADB\), \(AC = AD\), \(\angle CAB=\angle DAB\), \(AB = AB\) (common side).

Step2: Apply congruence postulate

By the Side - Angle - Side (SAS) congruence postulate.

24.

Step1: Identify sides

In \(\triangle MNP\) and \(\triangle MQP\), \(MN = MQ\), \(NP = QP\), \(MP = MP\) (common side).

Step2: Apply congruence postulate

By the Side - Side - Side (SSS) congruence postulate.

Answer:

1. SSS
2. SSS
3. SAS
4. HL
5. HL
6. SAS
7. SAS
8. SSS