Geometry is my favourite math unit – it relates to the real world, there are all kinds of manipulatives and students tend to enjoy it as well. This is how I like to introduce/review triangles with my grade 8 math students (this could suit any grade, the expectations would just differ):
Lesson One: Grade 8: Geometry Introduction/Review 
Curriculum Connections:

Minds On (10 mins): Mini Number Talk
I love this website: http://wodb.ca/index.html I project it on the board, and I choose the “shapes” category. Then I ask students to think independently about which shape doesn’t belong. After some time, I ask them to share with their group which one doesn’t belong, and that they need to use mathematical reasoning. Then, as a group they need to agree on which one, and why – then each group will share with the class. I use some of these questions to prompt discussion: “Why did you choose that one?” “Do you agree?” “Do you disagree? Why?” “Which answer is the most correct? Is there one?” 
Action (20 mins):
Students should work in pairs Each pair receives some triangles (I’ve used pattern blocks, paper cut outs, tangrams etc.), a protractor and a ruler. I ask each pair to categorize their shapes – based on whichever characteristics they’d like – but that they have to have mathematical justifications (not: blue and red etc.) Once they’ve finished, I ask them to join up with another pair and to justify their sorting, after sharing, they must combine their triangles with that pair and come up with new sorting rules/characteristics. I leave some discussion prompts on the board: “Measure all the angles and sides on your triangles” “Can you classify them in a different way?” “What do you notice about the sum of all the angles of a triangle?” 
Consolidate/Debrief (10 mins):
I like to bring the students back together to share what they’re thinking, things that they found and the rules they used to classify their shapes. I have groups share their classifications and groupings. 
Assessment:
Because this is a formative and introductory activity, I usually circulate throughout to make sure students are on the right track, looking for previous knowledge and misunderstandings etc. I am also looking for their ability to use protractors, think about angles and find relationships between characteristics in triangles. 
This is fun, handson and the students are doing most of the talking – which makes students and teachers happy!