صفحة 238 - كتاب الرياضيات - الصف 10 - الفصل 2 - المملكة العربية السعودية

الفصل 8

دليل الدراسة والمراجعة

8-3 الأقواس والأوتار (ص 194-200)

مثال 3 جبر: في E، إذا كان EF = EG، فأوجد AB. الوتران AB, CD متطابقان، لأن بعديهما عن E متساويان. إذن: AB = CD (النظرية 8.5) بالتعويض 3x - 9 = 2x + 3 بإضافة 9 لكلا الطرفين 3x = 2x + 12 بطرح 2x من كلا الطرفين x = 12 إذن: AB = 3(12) - 9 = 27

أوجد قيمة x في الشكل المجاور.

في K، إذا كان: MN = 16, mMLN = 98°، فأوجد كل قياس مما يأتي مقربًا إجابتك إلى أقرب جزء من مئة.

بستنة: يبين الشكل عريشًا يعلوه قوس من دائرة، إذا كان CD جزءًا من قطرها و AB يساوي 28% من الدائرة كاملة، فأوجد mCB.

8-4 الزوايا المحيطية (ص 201-207)

مثال 4 أوجد m∠D و m∠B. بما أن ABCD محاط بدائرة، إذن الزاويتان المتقابلتان متكاملتان. (تعريف الزوايا المتكاملة) m∠D + m∠B = 180° بالتعويض (23x + 12)° + (21x - 8)° = 180° بالتبسيط (44x + 4)° = 180° بالطرح 44x = 176 بالقسمة x = 4 إذن: m∠D = (23(4) + 12)° = 104° و m∠B = (21(4) - 8)° = 76°

أوجد كلا من القياسين الآتيين:

شعارات: إذا كان m∠1 = 42° في الشعار المجاور، فأوجد m∠5.

238 الفصل 8 الدائرة

وزارة التعليم Ministry of Education 2025 - 1447

الفصل 8 دليل الدراسة والمراجعة 8-3 الأقواس والأوتار (ص 194-200) --- SECTION: 3 --- مثال 3 جبر: في E، إذا كان EF = EG، فأوجد AB. الوتران AB, CD متطابقان، لأن بعديهما عن E متساويان. إذن: AB = CD (النظرية 8.5) بالتعويض 3x - 9 = 2x + 3 بإضافة 9 لكلا الطرفين 3x = 2x + 12 بطرح 2x من كلا الطرفين x = 12 إذن: AB = 3(12) - 9 = 27 --- SECTION: 19 --- أوجد قيمة x في الشكل المجاور. --- SECTION: 20 --- في K، إذا كان: MN = 16, mMLN = 98°، فأوجد كل قياس مما يأتي مقربًا إجابتك إلى أقرب جزء من مئة. 20. mNJ 21. LN --- SECTION: 22 --- بستنة: يبين الشكل عريشًا يعلوه قوس من دائرة، إذا كان CD جزءًا من قطرها و AB يساوي 28% من الدائرة كاملة، فأوجد mCB. 8-4 الزوايا المحيطية (ص 201-207) --- SECTION: 4 --- مثال 4 أوجد m∠D و m∠B. بما أن ABCD محاط بدائرة، إذن الزاويتان المتقابلتان متكاملتان. (تعريف الزوايا المتكاملة) m∠D + m∠B = 180° بالتعويض (23x + 12)° + (21x - 8)° = 180° بالتبسيط (44x + 4)° = 180° بالطرح 44x = 176 بالقسمة x = 4 إذن: m∠D = (23(4) + 12)° = 104° و m∠B = (21(4) - 8)° = 76° --- SECTION: 23 --- أوجد كلا من القياسين الآتيين: 23. m∠1 24. mGH --- SECTION: 25 --- شعارات: إذا كان m∠1 = 42° في الشعار المجاور، فأوجد m∠5. 238 الفصل 8 الدائرة وزارة التعليم Ministry of Education 2025 - 1447 --- VISUAL CONTEXT --- **DIAGRAM**: Circle with Chords AB and CD Description: A circle with center E. Two chords AB and CD are shown. Perpendicular segments EG to chord AB and EF to chord CD are drawn from the center E, indicating they are distances from the center to the chords. The length of chord AB is represented by the algebraic expression 3x-9. The length of chord CD is represented by the algebraic expression 2x+3. It is stated that the lengths of the perpendicular segments from the center to the chords are equal, i.e., EF = EG. Key Values: [object Object] Context: This diagram illustrates the theorem that if two chords in a circle are equidistant from the center, then the chords are congruent. This property is used to set up an equation (3x-9 = 2x+3) to solve for x and then find the length of chord AB. **DIAGRAM**: Circle with Parallel Chords Description: A circle containing two parallel chords. The arc intercepted between the chords on the upper-left side measures 142 degrees. The arc intercepted between the chords on the lower-right side also measures 142 degrees. A segment of one chord is labeled with the expression 3x+7, and a segment of the other chord is labeled with the expression 5x-9. Key Values: [object Object], [object Object] Context: This diagram is used to find the value of x based on the properties of parallel chords in a circle, specifically that parallel chords intercept congruent arcs, and segments of parallel chords between the same arcs are equal. **DIAGRAM**: Circle with Chord MN and Center K Description: A circle with center K. A chord MN is shown. A radius KJ extends from the center K to a point J on the circle. A segment KP is drawn from the center K to the chord MN, such that KP is perpendicular to MN. The length of segment KP is 10 units. The length of the chord MN is 16 units. Point L is on the circle, forming arc MLN. Key Values: [object Object] Context: This diagram is used to find arc measures (mNJ) and segment lengths (LN) using properties of chords and radii, specifically that a radius perpendicular to a chord bisects the chord and its intercepted arc. **DIAGRAM**: Circular Trellis Design Description: A circular design, possibly representing a garden trellis or an architectural element, with an internal grid pattern. The question refers to arcs AB and CD within this circle, where CD is part of its diameter and arc AB is 28% of the full circle. Key Values: [object Object] Context: This diagram is used to calculate arc measures based on given percentages of the circle and properties of diameters, specifically to find the measure of arc CB. **DIAGRAM**: Cyclic Quadrilateral ABCD Description: A circle with an inscribed quadrilateral ABCD. The measure of angle B is represented by the expression (21x-8) degrees. The measure of angle D is represented by the expression (23x+12) degrees. Angles B and D are opposite angles in the cyclic quadrilateral. Context: This diagram illustrates the theorem that opposite angles of a cyclic quadrilateral are supplementary (sum to 180 degrees). This property is used to set up an equation to solve for x and then find the measures of angles D and B. **DIAGRAM**: Circle with Inscribed Angle 1 Description: A circle with an inscribed angle labeled '1'. The arc intercepted by this angle measures 218 degrees. Key Values: [object Object] Context: This diagram is used to find the measure of an inscribed angle (m∠1) given the measure of its intercepted arc, using the inscribed angle theorem (the measure of an inscribed angle is half the measure of its intercepted arc). **DIAGRAM**: Circle with Inscribed Angle 28° Description: A circle with an inscribed angle measuring 28 degrees. The arc intercepted by this angle is labeled GH. Context: This diagram is used to find the measure of an intercepted arc (mGH) given the measure of its inscribed angle, using the inscribed angle theorem (the measure of the intercepted arc is twice the measure of the inscribed angle). **DIAGRAM**: Circular Emblem with Angles Description: A complex circular emblem or logo with a star at its center. Multiple lines intersect within the circle, forming various triangles and angles. Several angles are labeled with numbers 1, 2, 3, 4, and 5. The question states that the measure of angle 1 (m∠1) is 42 degrees. Key Values: [object Object] Context: This diagram is used to find the measure of angle 5 (m∠5) based on the given measure of angle 1 (m∠1 = 42°) and geometric properties of angles formed by intersecting chords or lines within a circle, possibly involving inscribed angles or angles formed by tangents/secants.