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#### Resources tagged with Perpendicular lines similar to Isosceles Reduction:

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##### Other tags that relate to Isosceles Reduction
Quadratic equations. Isosceles triangles. Area. Pythagoras' theorem. Inscribed circle. Radius (radii) & diameters. Cosine rule.

### There are 10 results

Broad Topics > 2D Geometry, Shape and Space > Perpendicular lines

### Three Way Split

##### Stage: 4 Challenge Level:

Take any point P inside an equilateral triangle. Draw PA, PB and PC from P perpendicular to the sides of the triangle where A, B and C are points on the sides. Prove that PA + PB + PC is a constant.

### A Shade Crossed

##### Stage: 4 Challenge Level:

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

### Tricircle

##### Stage: 4 Challenge Level:

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .

### At Right Angles

##### Stage: 4 Challenge Level:

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

### Quads

##### Stage: 4 and 5 Challenge Level:

The circumcentres of four triangles are joined to form a quadrilateral. What do you notice about this quadrilateral as the dynamic image changes? Can you prove your conjecture?

### Angle Trisection

##### Stage: 4 Challenge Level:

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

### Shrink

##### Stage: 4 Challenge Level:

X is a moveable point on the hypotenuse, and P and Q are the feet of the perpendiculars from X to the sides of a right angled triangle. What position of X makes the length of PQ a minimum?

### Perpendicular Lines

##### Stage: 4 Challenge Level:

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

### Similarly So

##### Stage: 4 Challenge Level:

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

### Right Time

##### Stage: 3 Challenge Level:

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?