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GCSE: Congruent Triangles

GCSE: Congruent Triangles. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Associated Resources: GCSEQuestions-Congruence.doc. Last modified: 18 th March 2014. What is congruence?. These triangles are similar . These triangles are congruent . ?. ?. They are the same shape .

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GCSE: Congruent Triangles

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  1. GCSE: Congruent Triangles Dr J Frost (jfrost@tiffin.kingston.sch.uk) Associated Resources: GCSEQuestions-Congruence.doc Last modified: 18th March 2014

  2. What is congruence? These triangles are similar. These triangles are congruent. ? ? They are the same shape. They are the same shape and size. (Only rotation and flips allowed)

  3. Proving congruence GCSE papers will often ask for you to prove that two triangles are congruent. There’s different ways in which we could show this: a ? SAS Two sides and the included angle. b ? ASA Two angles and a side. c ? SSS Three sides. ? d RHS Right-angle, hypotenuse and another side.

  4. Proving congruence Why is it not sufficient to show two sides are the same and an angle are the same if the side is not included? Try and draw a triangle with the same side lengths and indicated angle, but that is not congruent to this one. Click to Reveal In general, for “ASS”, there are always 2 possible triangles.

  5. What type of proof For triangle, identify if showing the indicating things are equal (to another triangle) are sufficient to prove congruence, and if so, what type of proof we have. This angle is known from the other two.  SSS SAS  SSS SAS  SSS SAS ASA RHS ASA RHS ASA RHS  SSS SAS  SSS SAS  SSS SAS  SSS SAS ASA RHS ASA RHS ASA RHS ASA RHS

  6. GCSE Question Q1 Bro Tip: The general strategy is to use the information to mark sides that are the same on the diagram, then recreate this verbally by comparing pairs of sides on the congruent triangles. ? • LM = BN as LMNB is a parallelogram. • BN = NC as N is the midpoint of BC, thus LM = NC. • Similarly, BL = NM as LMNB is a parallelogram, and BL = LA as L is the midpoint of BA, so LA = NM. • AM = MC as M is the midpoint of AC. • All 3 sides are the same, therefore ALM is congruent to MNC by “SSS”. Bro Tip: Mark schemes require a conclusion, and use the acronyms SSS, ASA, etc.

  7. Exercises Q2 Bro Tip: Choose which congruency proof you’re going to use from the outset. AB = AC (equilateral triangle) AD is common. ADC = ADB = 90. Therefore triangles congruent by RHS. ? BD = DC as congruent triangles. BC = AB as equilateral triangle. Therefore BD = ½ AB ?

  8. Exercises Q3 AD = CD as equal sides. AB = BC as equal sides. BD is common. Therefore ∆ADB is congruent to ∆CDB by SSS. ?

  9. Exercises Edexcel June 2006 BC = CE equal sides CF = CD equal sides BCF = DCE = 150o BFC is congruent to ECD (SAS) ? ? So BF=ED (congruent triangles) BF = EG ( opp sides of parallelogram) (2)

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