Congruency, SMB-013
Which two of the triangles below are congruent? (2 marks)
Congruency, SMB-012
Which two of the triangles below are congruent? (2 marks)
Congruency, SMB-015
Congruence, SMB-014
Congruency, SMB-011
The diagram shows a circle with centre `O` and radius 5 cm.
The length of the arc `PQ` is 9 cm. Lines drawn perpendicular to `OP` and `OQ` at `P` and `Q` respectively meet at `T`.
Prove that `Delta OPT` is congruent to `Delta OQT`. (2 marks)
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Congruency, SMB-010
In the diagram, `AD` is parallel to `BC`, `AC` bisects `/_BAD` and `BD` bisects `/_ABC`. The lines `AC` and `BD` intersect at `P`.
- Prove that `/_BAC = /_BCA`. (1 mark)
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- Prove that `Delta ABP ≡ Delta CBP`. (2 marks)
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Congruency, SMB-008
In the figure below, \(ABCD\) is a parallelogram where opposite sides of the quadrilateral are equal.
Prove that a diagonal of the parallelogram produces two triangles that are congruent. (2 marks)
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Congruency, SMB-007
In the figure below, \(AB \parallel DE, \ AC = CE\) and the line \(AE\) intersects \(DB\) at \(C\).
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-006
In the quadrilateral \(ABCD\), \(AB \parallel CD, \angle BAD = \angle BCD\) and \(\angle DBC = \angle BDA = 90^{\circ} \).
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-005
In the figure below, \(BE = BC\), \(AB = BD\) and the line \(AD\) intersects \(CE\) at \(B\).
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-004
In the circle below, centre \(O\), \(OB\) is perpendicular to chord \(AC\).
Prove that a pair of triangles in this figure are congruent. (2 marks)
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Congruency, SMB-003
In the figure below, the line \(AD\) intersects \(BE\) at \(C\), \(BC = CD\) and \(AC = EC\).
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-002
The diagram shows two triangles that touch at the middle of a circle.
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-001
The diagram shows two right-angled triangles where \(\angle BAC = \angle BDC = 90^{\circ}\), and \(AB = BD\).
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-009
The diagram shows a right-angled triangle `ABC` with `∠ABC = 90^@`. The point `M` is the midpoint of `AC`, and `Y` is the point where the perpendicular to `AC` at `M` meets `BC`.
Show that `\Delta AYM \equiv \Delta CYM`. (2 marks)
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Plane Geometry, 2UA 2018 HSC 12c
The diagram shows the square `ABCD`. The point `E` is chosen on `BC` and the point `F` is chosen on `CD` so that `EC = FC`.
- Prove that `Delta ADF` is congruent to `Delta ABE`. (2 marks)
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- The side length of the square is 14 cm and `EC` has length 4 cm. Find the area of `AECF`. (2 marks)
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Plane Geometry, 2UA 2017 HSC 15a
The triangle `ABC` is isosceles with `AB = AC` and the size of `/_BAC` is `x^@`.
Points `D` and `E` are chosen so that `Delta ABC, Delta ACD` and `Delta ADE` are congruent, as shown in the diagram.
Find the value of `x` for which `AB` is parallel to `ED`, giving reasons. (3 marks)
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