**Hey, look at this symbol – ≅**

If your students or kids look at this symbol and think someone put some toothpaste on an equality sign, they are not alone.

Using statements and some simple set of rules to find whether two triangles will completely coincide when put above each other or not is definitely an interesting application of math.

But it isn’t always the easiest one.

Teaching the same concept by including various interactive components like competitions, and arts and crafts that encourage hands-on learning can certainly help make it much more simpler and fun. This blog enlists several activities that will enable the students to prove congruence in interesting and exciting ways.

**Learning triangle congruency through activities**

Just like many triangle games and manipulatives, make learning enjoyable and the conceptual knowledge of congruence palatable, here’s a list of a few activities that you can do and learn with your class.

**1. Cut and match**

For this activity, this educator will have to draw differently shaped, unaligned, and randomly placed triangles on a sheet. This can be done digitally as well and then the sheets can be printed out such that each student gets one. The educator will also need to arrange several student-friendly scissors or other safe paper-cutting instruments.

The goal of the students in this activity would be to cut the different triangles and see which one completely overlaps with another. They will then be given certain properties about the triangles that will further help them prove which triangles are congruent with one another.

This activity will help students in understanding the basics of the principle of congruence and what it means as well as how to prove it.

**2. Designer page**

For this activity as well, the educator needs to arrange some student-friendly paper-cutting and pasting instruments.

Here, soon after the students are done learning about a new condition for finding congruence, they will be asked to represent the same in their notebooks. They will do so by cutting, folding, and pasting the page right after their notes about that particular condition end. For example, for the RHS condition, the students will cut the page and fold it to make two congruent right-angled triangles.

Not just pictorially but physically engaging in the activity of making congruent triangles will help the students better understand and remember the various conditions for congruence.

**3. Prove it**

For this activity, the educator will have to make a bowl full of triangles with various properties written on them like their angles, length of their sides, etc.

The class will be divided into 4-5 teams. One student from each team will go up one by one and pick out two triangles at random. They will be given time to assess the triangles. Their task, as a team, will be to come up with proof and present the same on the board proving or disproving the congruence of two triangles based on their properties. The team that correctly proves the most number of assertions will be declared the winner.

This activity will involve group learning and team participation to help analyze various properties of the triangles and arrive at the correct proof while backing it all up with evidence.

**4. Jigsaw with a twist**

For this activity, the educator will need to write down the proof of congruence based on different conditions for four pairs of triangles. Then they will have to cut this proof up step by step into chits and mix the chits up in two bowls. This should be done in such a way that each bowl has mixed-up chits with steps written for two proofs.

The class will be divided into two teams with an equal number of students in each. They will each be given the bowls with steps and the four sets of triangles will be drawn on the board. Here the task of the students will be to look at the sets of triangles and arrange the steps of the proof such that it proves two pairs represented on the board are congruent. The first team to figure out which triangles’ proof they have and correctly arrange it will win.

This game will introduce competitiveness to learning, making it more fun and engaging for students. They will have to reconstruct the proof step by step which will require a fair amount of exercise of their deductive skills and congruent conceptual knowledge.

**5. Mix and match**

For this activity, the educator will have to make congruent triangles in pairs with different conditions of congruence. They will then have to put various sets of these triangles in a bowl.

The task of the students here will be to walk up to the bowl and pick a pair at random. The properties of the triangles that helped prove that they are congruent will be mentioned in the triangles. Based on what is mentioned, the students will then place the pair of triangles depending on the condition that proves their congruence.

For example, if the pair of triangles the student picked has two equal sides and the angle between those sides for both the triangles is 40 degrees, this means the triangles are congruent based on the Side-Angle-Side condition and will be placed in the SAS pile by the student.

This activity will help students in understanding, learning, and applying various conditions of congruence without even needing a pen and paper to write it all down to prove it.

**6. Under my seat**

For this activity, the educator will have to prepare several pairs of congruent triangles. These triangles should then be mixed together and randomly placed under the seats of the students.

The task of the students here will be to pick the triangle placed under their seat and find it’s congruent among their classmates.

They will have to go around seeing the properties of the triangles of various classmates to see if they are congruent with their triangles under any condition of congruence. The first three pairs to successfully find their congruent partners should be awarded.

This activity will also require the students to use their knowledge of various conditions of congruence to eliminate the triangles that don’t meet any as fast as possible and find their congruent partner in a limited time.

**7. Similarity or congruence?**

For this activity, the educator will need to prepare several pairs of triangles with different properties mentioned and a screen to present these triangles on.

The class will be divided into two teams with equal students on each team. Turn by turn, the teams will be shown a pair of triangles and their task will be to tell if they are similar or congruent and under which condition. For example, two triangles having three angles of 80 degrees, 50 degrees, and 50 degrees will be similar under the Angle-Angle-Angle condition. In the end, the team with the highest number of correct answers will win.

This game will encourage the students to learn the difference between similarity and congruence as well as various conditions that prove them.

**8. Who am I?**

For this game, the educator will have to prepare cards with various conditions of congruence written on them.

The class will be divided into two teams with equal students in each. One member from each team will go pick a card and without seeing what it is, hold it up against their forehead so that the class can see the condition of congruence mentioned. Then, the task of the team members would be to describe a pair of triangles and their properties to help their team members guess the condition they are holding. The team to successfully guess it first will get the point and the team with the highest points will win.

For understanding the condition they are holding against their forehead based on the triangles described by their team, the student will have to mentally figure out what condition of congruence fits these triangles. This activity will require quite a bit of teamwork as well as sound congruence condition knowledge.

**9. Color me mine**

For this activity, the educator will have to design a coloring sheet full of abstract figures, including scattered triangles. This can be made digitally after which the educator can take printouts to give to each student. The educator will also have to arrange a set of colors for every student.

Every congruence condition will have its own assigned color. The task of the students here will be to fill in the colors based on the congruence condition a pair of triangles fulfills.

This activity will make assessing students on their understanding of different conditions of congruence and their application a lot more enjoyable.

**10. Give me a reason**

For this activity, the educator will have to prepare a series of assertions and reasons. For example, the assertion could be that Triangle ABC is congruent to Triangle PQR. One of the many possible correct reasons for this assertion could be that Side AB=PQ, Side BC=QR, and Side CA=RP. This will prove that Triangle ABC is congruent to Triangle PQR under the Side-Side-Side condition. This will then need to be jumbled up and digitally presented to students on a screen.

The class will be divided into 5 teams with an equal number of students in each. The task of the students here will be to buzz whenever they see a match between the presented reasons and assertions. The first team to buzz will get to answer one match. If they match it correctly, they’ll get a point and if not, the chance to answer will be passed on to the team that buzzed second. At the end of the game, the team with the highest points will win.

This game will make the task of learning how to successfully prove a claim and back one’s assertions with reason more challenging yet interesting.

**Conclusion**

Congruence can be a tricky concept to understand and learn with all its different conditions and whatnot. But, learning can always be made fun using some simple but exciting games and activities.

The games that have been mentioned above do exactly that by including various components of arts, and crafts, competitions, quizzes, and much more, to make learning more hands-on and interactive.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder ofSmartynote -‘The notepad app for dyslexia’,