Kites · Grade 9
In Kites (Grade 9) you practise 3 skills: Angles in a kite · The diagonals of a kite · A kite on a coordinate grid. A kite is a quadrilateral with two pairs of equal adjacent sides. The diagonal joining the two vertices between the equal sides is the main diagonal, and it is the kite's line of symmetry: it bisects the two angles at its ends, and the other two angles are equal. The angles of a quadrilateral add up to 360°, so when you know the two angles on the main diagonal, each of the other two is half of what is left of 360°.
The diagonals of a kite are perpendicular, and the main diagonal bisects the other one. So they split the kite into four right triangles, and Pythagoras' theorem works in them: half the shorter diagonal and a part of the main diagonal give a side. The area of a kite is the product of its diagonals divided by 2. On a coordinate grid, when the main diagonal lies on the vertical axis, the fourth vertex is the reflection of the opposite vertex in that axis. To check whether a quadrilateral is a kite, compare the adjacent sides: work out their squared lengths and see whether they are equal.
Tip: Draw the main diagonal first: it splits the kite into two congruent triangles, and whatever is true on one side is true on the other.
What you learn
Angles in a kite
For example: In the kite ABCD the adjacent sides are equal: AB = AD, CB = CD . Given ∢B = 75°, ∢C = 160°, ∢D = 75° . Find ∢A .
Answer and solution
The answer: 50 °
The side angles are equal, so: ∢A = 360° − 75° − 160° − 75° = 50°
The diagonals of a kite
For example: In the kite ABCD the adjacent sides are equal: AB = AD, CB = CD . The diagonals meet at O , and BD = 6 cm. Find BO .
Answer and solution
The answer: 3 cm
The main diagonal bisects BD : BO = 6 ÷ 2 = 3
A kite on a coordinate grid
For example:
The points A(0, 2), B(4, −6), C(0, −8) are vertices of the kite ABCD . Its main diagonal AC lies on the vertical axis. What are the coordinates of D ?Answer and solution
The answer: (−4, −6)
A reflection in the vertical axis: the first coordinate changes sign and the second stays. D(−4, −6)
Not on the site yet
Parts of this topic that are not built yet: Proving the properties of a kite · Concave kites (arrowheads).
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the Israeli Ministry of Education's grade 9 maths curriculum (2026–27).