Topic 7 Year 9 Mathematics
Mathematics | |||
Topic | Constructions, congruence and loci | ||
No of lessons | 8 | ||
When is it happening | Term 2 | ||
What will students learn |
Understand that circles can be used to draw the locus of points that are a given distance from a point – Be able construct perpendicular and angle bisectors – Experience constructing perpendicular and angle bisectors within a geometric problem – Understand congruency conditions for triangles – Be able to identify when two triangles are congruent – Experience using congruent triangles to prove other geometric results |
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Key Knowledge that students should know at the end of 'Topic' | This is the knowledge that students will meet for the first time in this topic | Students use circles to represent the locus of points that are a given distance from a point. Students describe the locus of specific points on the circumference of circles. Students develop this idea to use circles with the same radius to find points that are equidistant from two points. The perpendicular bisector of a line segment between two points is constructed by connecting points that are equidistant from them. The angle bisector is constructed using the perpendicular bisector of a line segment that connects points that are equidistant from the angle. Students construct triangles given a side and an angle. This can be done by either giving the side length that encloses the angle or by giving the angle at the opposite end of the given side. The two ways for constructing triangles from the previous lesson (SAS and ASA) are combined with SSS. These three constructions are used as three sets of conditions that give congruent triangles. The conditions for congruence are used to prove other geometric results. We can use congruent triangles to prove the construction for an angle bisector. | |
This is knowledge that students may have met before but will need to deepen their understanding |
Student revisit constructing a triangle using a compass |
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Key Skills that students should be able to demonstrate at the end of 'Topic' | This is the skills that students will meet for the first time in this topic | Identify points, lines and planes | |
This is skills that students may have met before but will need to develop | Use segments and congruence | ||
Key vocabulary that students should know and understand | |||
The Big Question | What is the difference between construction and Loci? | ||
Key questions that students should be able to answer at the end of the 'Topic' |
Can you describe the locus of a point relative to another point? | ||
Can you find two points that are equidistant from two given points? | |||
Can you construct the perpendicular bisector of a line connecting two points? | |||
Can you construct an angle bisector? | |||
Can you construct triangles given SAS and ASA? | |||
Can you identify triangles that are congruent? | |||
Can you prove when two triangles are congruent using geometric properties? | |||
Can you use perpendicular and angle bisectors to construct angles of a given size? |