Mathematics
Geometry and Measurement
Geometry and measurement here covers four topics: shapes, sizes and patterns for the early years (ages 3 to 5), measurement, area and perimeter in grade 5, the Pythagorean theorem in grade 8, and trigonometry in the right triangle in grade 10. Each is taught as a live lesson with Lessi, an AI teacher, at the student's own pace.
- Topics
- 33
- Ages
- Grade 10 – Grade 12
Areas of Mathematics
Topics in Geometry and Measurement1–24 of 33
- How do you prove two triangles are congruent?To prove two triangles are congruent, show that three specific corresponding pairs of sides and angles are equal using an established congruence theorem: Side-Angle-Side…Read the topic
- How do you find the ratio of areas of similar triangles?The ratio of the areas of two similar triangles equals the square of the ratio of their corresponding sides. If the side length ratio, or scale factor, of triangle A to…Read the topic
- What is the relationship between central and inscribed angles?When a central angle and an inscribed angle intercept the same arc of a circle, the measure of the central angle is twice the measure of the inscribed angle. Conversely,…Read the topic
- Why are tangents from an outside point equal?Tangents drawn to a circle from the same outside point are equal in length because they form two congruent right triangles. When you connect that external point to the…Read the topic
- Why do opposite angles of a cyclic quadrilateral add up to 180 degrees?The opposite angles of a cyclic quadrilateral add up to 180 degrees because each opposite angle intercepts one of two arcs that together make a full 360-degree circle. By…Read the topic
- Why does the ratio between sides depend only on the angle?The ratio between sides in a right triangle depends entirely on the acute angle because fixing that angle locks all three angles to add up to 180 degrees. By Angle-Angle…Read the topic
- What are sine, cosine and tangent?Sine, cosine, and tangent are trigonometric ratios that relate the angles of a right triangle to its side lengths. For any acute angle, sine is the opposite side divided…Read the topic
- How do you find a side length when the angle is known?To calculate a side length when an angle is known, choose the trigonometric ratio connecting your known side and desired side: sine for opposite and hypotenuse, cosine…Read the topic
- How do you find an angle when two sides are known?To find an angle when two sides are known, divide the two side lengths to find their ratio, determine whether that ratio is sine, cosine, or tangent relative to the…Read the topic
- What are the special angles in trigonometry?The special angles in trigonometry are 30°, 45°, and 60°. Their exact sine, cosine, and tangent values derive from an isosceles right triangle and an equilateral triangle…Read the topic
- What is the difference between an angle of elevation and an angle of depression?Both angles are measured from a flat horizontal line of sight. An angle of elevation is formed when looking upward toward an object, while an angle of depression is…Read the topic
- How to use trigonometry in an isosceles triangle?You can apply trigonometry to an isosceles triangle by dropping an altitude from the apex to the base. This altitude splits the shape into two congruent right triangles,…Read the topic
- How to solve trigonometry word problems?Tackle trigonometry word problems by sketching the scenario as a right triangle and labeling the known sides and angles. Identify whether you need sine, cosine, or…Read the topic
- How to find the distance between two points?You find the distance between two points (x1, y1) and (x2, y2) by applying the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). First, subtract the x-coordinates…Read the topic
- How do you find the equation of a line from a point and a slope?Use point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the known point. Substitute the values of m, x1, and y1 into the…Read the topic
- How to find parallel and perpendicular slopes?To find parallel and perpendicular slopes, first write the given line in slope-intercept form, y = mx + b, to identify its slope, m. Parallel lines have identical slopes,…Read the topic
- How do you find the distance from a point to a line?You find the perpendicular distance from a point (x₀, y₀) to a line written in general form Ax + By + C = 0 using the formula d = |Ax₀ + By₀ + C| / √(A² + B²). The…Read the topic
- How do you find the center and radius of a circle?To find the center and radius of a circle, write its equation in standard form: (x - h)^2 + (y - k)^2 = r^2. The center is the point (h, k) and the radius is r, which is…Read the topic
- How do you find the points of intersection between a line and a circle?To find the points of intersection between a line and a circle, solve the linear equation for one variable and substitute it into the circle's equation. This forms a…Read the topic
- How do you find the equation of a tangent to a circle at a given point?To find the equation of a tangent to a circle at a given point, first find the circle center. Calculate the slope of the radius connecting the center to the contact…Read the topic
- How to prove a quadrilateral is a parallelogram with coordinates?To prove a quadrilateral is a parallelogram with coordinates, show either that both pairs of opposite sides have equal slopes, or that the two diagonals share the exact…Read the topic
- How do you convert degrees to radians?Multiply the angle in degrees by pi divided by 180 degrees (pi / 180) to convert the measurement into radians. Next, simplify the fraction to express the angle in exact…Read the topic
- How to find sine and cosine on the unit circle?You find sine and cosine on the unit circle by looking at the coordinates where an angle's terminal side lands on a circle of radius 1 centered at the origin. The…Read the topic
- How to graph sine cosine and tangent?Graphing sine, cosine, and tangent is done by plotting key values from the unit circle across radians. Sine starts at (0, 0), peaks at (π/2, 1), and repeats every 2π.…Read the topic
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Featured teacher דביר הראלMathematics teacher₪200 / hourרמת גןבואו להתחיל איתי את השנה החדשה בתחושת ביטחון עצמי והבנה מעמיקה של החומר! אצלי גדלים מנצחים. אני הייטקיסט בעל רקע רב שנים בהוראת מתמטיקה בתיכון, מדעי המחשב ואנגלית.Full profile
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יוחאי אMathematics teacherרמת גןסטטיסטיקאי ומוסמך MBA מסייע בעיבודים סטטיסטיים ומעביר שיעורים פרטיים (ליחיד או לקבוצות קטנות).Full profile
גל חכם אהרוןMathematics teacher₪150 / hourירושליםבוגרת תואר ראשון במשפטים ובכלכלה מהאוניברסיטה העברית, ומרצה במכינה האוניברסיטאית של האוניברסיטה העברית.Full profile
אופיר מאגדיMathematics teacher₪200 / hourתל אביב -יפופרונטלי+ZOOM. הכנה מהירה ותכליתית לבחינה! מורה פרטי מצוין!!! רק למקצועות: המימון, ניהול פיננסי, שוק ההון ושמאות מקרקעין. יש מאות המלצות!Full profile
ראובן לוריאMathematics teacher₪145 / hourנתניהנעים מאוד, ראובן :) הייתי מתכנת עד לפני שנתיים, פרשתי כדי להתמקד בהוראה פרטית מותאמת אישית.Full profile
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נועה טלMathematics teacher₪130 / hourתל אביב -יפומורה פרטית לביולוגיה, מתמטיקה ומדעי המחשב. BSc בביולוגיה ומדעי המחשב + MSc בהנדסה (אונ׳ תל אביב)Full profile
About Geometry and Measurement
The line starts with circles, squares and triangles, corners and sides, and patterns that repeat like a song. In grade 5 it turns to measuring: choosing a unit, the perimeter around a shape, area and then volume. In grade 8 the Pythagorean theorem goes from square roots to the distance between two points on the coordinate plane. In grade 10, sine, cosine and tangent are built from similar triangles and used to reach heights that cannot be measured directly.
Lessi explains each step on a board and out loud, then checks it with a short quiz before moving on, so a gap shows up while it is still small. The first 60 minutes with Lessi are free with an account, which is enough to try a whole lesson first.