TMUA Triangles and Congruency
TMUA likes testing this topic - for example whether given various criteria a triangle is uniquely congruent or not. It also assumes students are completely familiar with congruent and similar triangles, and spotting them to solve geometric questions. We include here the Cosine and Sine Rules, both of which are tested and need to be known by heart (no formula booklets are allowed in TMUA).
For those so interested, we offer both one to one TMUA coaching on triangles and congruency, as well as online group coaching via Zoom - 'TMUA Geometry and Shapes' is Session #12 of 20' . Check our TMUA Group Coaching Schedule page for dates when these sessions are available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our 'Online Coaching FAQ'.
Feel free to contact us if you require more information regarding any of the above.
Free Revision Resources
The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions on triangles and congruency - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.
- Teaser #99 - tests ability to apply Heron's Formula to a triangle word problem (the final calculation is beyond TMUA) - Standard
- Teaser #41 - tests finding area of triangle given rhombus and square - Standard
- Teaser #95 - tests knowledge of how to split a pyramid in two by volume (involves similar triangles) - Standard
- Teaser #378 - tests finding the distance between two points on a composite shape - Standard
- Teaser #496 - tests criteria for which a triangle is described uniquely - Medium
- Teaser #425 - tests ability to spot two sets of similar triangles to find a length within a trapezium - Medium
TMUA Past Questions on Triangles and Congruency: 2016 p1 q20; 2016 p2 q9; 2016 p2 q16; 2017 p1 q6; 2017 p1 q20; 2018 p1 q19; 2018 p2 q14; 2021 p1 q15; 2021 p2 q18; 2022 p1 q14; 2022 p1 q17; 2023 p1 q8; 2023 p1 q16; 2023 p2 q8
Practice makes perfect - good luck in your studies!