What’s the same, what’s different? Starter What’s the same, what’s different?
Which coloured shape is mathematically similar to this white one?
Which coloured shape is mathematically similar to this white one?
Which coloured shape is mathematically similar to this white one?
Which coloured shape is mathematically similar to this white one?
Are these triangles similar? = yes, = no, = not sure 6 cm 10 cm 5 cm 3 cm 4 cm 8 cm
Are these squares similar? = yes, = no, = not sure 6 cm 2 cm 2 cm 6 cm
Are these rectangles similar? = yes, = no, = not sure 6 cm 2 cm 10 cm 4 cm
Are these rectangles similar? = yes, = no, = not sure 4 cm 5 cm 2 cm 10 cm
Are these shapes similar? = yes, = no, = not sure X cm 7 cm 3 cm 15 cm
What about if I tell you they ARE mathematically similar. X cm 7 cm Could you calculate x? 3 cm 15 cm
X cm 7 cm These two represent the same side 3 cm 15 cm
X cm 7 cm 3 cm 15 cm Write as a ratio 3 : 15 Simplify 1 : 5 This number is the scale factor 15 cm
x 5 35 cm X cm 7 cm 3 cm 15 cm
These two shapes are mathematically similar. Calculate x. Write as a ratio 8 : 12 Simplify 1 : 1.5 12 cm 8 cm 10 cm 15 cm x cm x 1.5
These two shapes are mathematically similar. Calculate x. Write as a ratio 10 : 25 Simplify 1 : 2.5 25 cm 10 cm 18 cm x cm 45 cm ÷ 2.5
Answers 1) x = 7.5 cm 2) x = 6.25 cm 3) x = 8.33 cm 4) x = 4.5 cm y = 7 cm 5) x = 11.2 cm y = 12.5 cm 6) x = 6.45 cm 7) x = 4 cm y = 1.5 cm 8) x = 4.5 cm y = 9 cm 9) x = 1.6 cm 10) x = 4.8 cm y = 5.33 cm
Starter Calculate a, b, c and d. sf 2 But 9 x 2 isn’t 36?!!!!!!!!!! 9 cm² 36 cm² 4 cm 2 cm b cm² d cm² c cm 4.5 cm a cm 9 cm But 9 x 2 isn’t 36?!!!!!!!!!!
Linear SF = 3 Area SF = 3² = 9 Volume SF = 3³ = 27 4cm Why? 12cm
160 Area = _____cm² Area = 40cm² 2 Linear SF = ___ 4 Area SF = ___ 6cm 12cm
648 Volume = ______cm³ Volume = 24cm³ 9 Area SF = ___ 3 Linear SF = ___ 27 Volume SF = ___ Surface area = 32cm² Surface area = 288cm²
Answers 1) Linear SF = 2 Area SF = 4 Volume SF = 8 2) Linear SF = 1.5 5a) 6 cm 5b) 3.375 6) 80 cm 7a) £17.62 7b) 3.92 or 4 people 8) 3.9 kg
What’s the same? What’s different? Starter What’s the same? What’s different? 4cm 42° 6cm 6cm 42° 9cm 4cm 6cm 42° 32° 8cm 4cm
Definitions Congruent shapes have all sides and angles equal. Similar shapes have all angles equal but one is an enlargement of the other.
Are these triangles congruent? Congruence Are these triangles congruent? For triangles to be congruent, three properties must be the same: SSS 6cm 6cm 4cm 3.5cm 4cm 3.5cm
Are these triangles congruent? Congruence Are these triangles congruent? For triangles to be congruent, three properties must be the same: SAS 4cm 3.5cm 78° 78° 4cm 3.5cm
Are these triangles congruent? Congruence Are these triangles congruent? For triangles to be congruent, three properties must be the same: ASA 47° 4cm 78° 47° 78° 4cm
Are these triangles congruent? Congruence Are these triangles congruent? For triangles to be congruent, three properties must be the same: RHS 5cm 5cm 4cm Right angle, hypotenuse, side 4cm
Are these triangles congruent?
Are these triangles congruent?
Are these triangles congruent?
Are these triangles congruent?
Are these triangles congruent?
Are these triangles congruent?
Are these triangles congruent?
Are these triangles congruent?
Are these triangles congruent?
PR = PQ (isosceles triangle) Angles RPQ = QPR (same angle) Diagram NOT accurately drawn Triangle PQR is isosceles with PQ = PR. X is a point on PQ. Y is a point on PR. PX = PY. Prove that triangle PQY is congruent to triangle PRX (Total 3 marks) PX = PY (as in question) PR = PQ (isosceles triangle) Angles RPQ = QPR (same angle) SAS proves triangles are congruent.
Create your own question on proving congruence or similarity. Plenary Create your own question on proving congruence or similarity. Make sure you have provided enough information on your diagram.