New
New
Year 10
•
Higher
Checking and securing understanding of congruent triangles (SAS)
I can understand and use the criteria by which triangles are congruent (SAS).
New
New
Year 10
•
Higher
Checking and securing understanding of congruent triangles (SAS)
I can understand and use the criteria by which triangles are congruent (SAS).
Lesson details
Key learning points
- By knowing two side lengths and the angle between them in the triangle and image, you can prove congruence.
- The angle between the sides must be the same in both object and image.
- The given sides must have the same multiplicative relationship.
Common misconception
Pupils may try and use this criteria without knowing the angle between the two sides.
Pupils can construct triangles with two sides and an angle to see that there are two potential triangles, and therefore congruency is not guaranteed with SSA.
Keywords
Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
If your pupils need further support or practice, consider the unit Geometrical properties: similarity and Pythagoras' theorem. Pupils working on the higher tier may want to concentrate their time on the second learning cycle.
Teacher tip
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Video
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Starter quiz
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6 Questions
Q1.
Sofia says, "If one shape can fit exactly on top of another using reflection, __________ or __________, then the shapes are congruent." Select the words that correctly complete Sofia's statement.
enlargement
Correct answer: rotation
rotation
similarity
transformation
Correct answer: translation
translation
Q2.
Which of these pairs of shapes are congruent to each other?
Correct Answer: An image in a quiz
Q3.
Some Oak pupils are discussing congruence. Which pupils are correct?
Correct answer: Aisha: "All circles are similar to each other."
Aisha: "All circles are similar to each other."
Alex: "All rhombi are similar to each other."
Jacob: "All isosceles triangles are similar to each other."
Laura: "All pentagons are similar to each other."
Correct answer: Sam: "All regular hexagons are similar to each other."
Sam: "All regular hexagons are similar to each other."
Q4.
The diagram shows a pair of congruent triangles. The length of the side marked $$y$$ is m.
Correct Answer: 9, nine
9, nine
Q5.
The diagram shows a pair of congruent triangles. Which of these Oak pupils are making a correct statement?
Correct answer: Alex: "The side marked $$x$$ is 108 mm."
Alex: "The side marked $$x$$ is 108 mm."
Andeep: "The angle marked $$w$$ is 53°."
Correct answer: Jacob: "The side marked $$y$$ is 66 mm."
Jacob: "The side marked $$y$$ is 66 mm."
Lucas: "The side marked $$z$$ is 66 mm."
Correct answer: Sofia: "The angle $$w$$° is 95°."
Sofia: "The angle $$w$$° is 95°."
Q6.
Select the statements needed to prove the following: "The diagonal of a kite bisects the shape into two congruent triangles."
AB = AD as they are opposite edges on a kite. Likewise BC = CD
Correct answer: AB = AD as they are adjacent edges on a kite. Likewise BC = CD
AB = AD as they are adjacent edges on a kite. Likewise BC = CD
Angle ABC = Angle ACD as a kite has one pair of equal angles
Correct answer: AC is a shared edge
AC is a shared edge
Correct answer: ∴ triangle ABC is congruent to triangle ADC by SSS.
∴ triangle ABC is congruent to triangle ADC by SSS.
Exit quiz
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6 Questions
Q1.
Jun says, "If one shape can fit exactly on top of another using rotation, __________ or __________ then the shapes are congruent." Select the words that correctly complete Jun's statement.
enlargement
Correct answer: reflection
reflection
similarity
Correct answer: translation
translation
transformation
Q2.
Some Oak pupils are discussing congruence. Which pupils are correct?
Correct answer: Andeep: "Two triangles are congruent if they have three edges the same."
Andeep: "Two triangles are congruent if they have three edges the same."
Izzy: "Two triangles are congruent if they have three angles the same."
Jun: "Two triangles are congruent if they have two edges and an angle the same."
Correct answer: Lucas: "No Jun, they must have two edges and the angle between them the same."
Lucas: "No Jun, they must have two edges and the angle between them the same."
Q3.
Are triangle ABC and DEF congruent? Explain your answer.
Correct answer: No, the angles between the two equal sides are different.
No, the angles between the two equal sides are different.
Yes, they have two equal sides, so the 3rd side is also fixed.
They are similar but not congruent.
Q4.
Given these two triangles are congruent, find the length of the sides marked $$x$$ and $$z$$.
Correct answer: Side $$x$$ is 8 cm
Side $$x$$ is 8 cm
Side $$x$$ is 15 cm
Side $$x$$ is 17 cm
Side $$z$$ is 15 cm
Correct answer: Side $$z$$ is 17 cm
Side $$z$$ is 17 cm
Q5.
Given these two triangles are congruent, the angle marked $$y$$ is °.
Correct Answer: 36
36
Q6.
ABCD is an isosceles trapezium. Select the statements needed to prove that triangle ABC and triangle ABD are congruent.
Correct answer: AD = BC as the trapezium is symmetrical. AB is a common edge
AD = BC as the trapezium is symmetrical. AB is a common edge
AC = BD as the trapezium is symmetrical. AB is a common edge
Correct answer: Angle DAB = angle ABC as the trapezium is symmetrical.
Angle DAB = angle ABC as the trapezium is symmetrical.
Correct answer: ∴ triangle ABC and triangle ABD are congruent by SAS.
∴ triangle ABC and triangle ABD are congruent by SAS.
∴ triangle ABC and triangle ABD are congruent by SSS.