From the Catechism of the Catholic Church:

V. THE MANY FORMS OF PENANCE IN THE CHRISTIAN LIFE

1438 The seasons and days of penance in the course of the liturgical year (Lent, and each Friday in memory of the death of the Lord) are intense moments of the Church’s penitential practice.[36] These times are particularly appropriate for spiritual exercises, penitential liturgies, pilgrimages as signs of penance, voluntary self-denial such as fasting and almsgiving, and fraternal sharing (charitable and missionary works).

Some ideas for doing penance on Fridays:

Fasting

• Fast with one full meal, no meat.

• Give up alcoholic beverages.

• Give up coffee.

• Give up all desserts.

• Fast from music, TV, Internet and phone time.

Prayer

• Pray the Rosary.

• Attend Holy Mass.

• Pray the Stations of the Cross.

• Do a Holy Hour.

• Meditate on the passion by reading the Gospels.

• Read a book on the Life of Christ. Some books you might want to read:

Life of Christ

Characters of the Passion: Lessons on Faith and Trust

The Agony of Jesus

The Dolorous Passion of Our Lord Jesus Christ

The Passion of Jesus and Its Hidden Meaning

The School of Jesus Crucified: The Lessons of Calvary in Daily Catholic Life

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