تأكد - كتاب الرياضيات - الصف 10 - الفصل 2 - المملكة العربية السعودية

تأكد

المثال 1 أوجد كل قياس مما يأتي:

1) m∠B

2) mRT

3) mWX

4) علوم: يبين الشكل المجاور انكسار أشعة الضوء في قطرة مطر لإنتاج ألوان الطيف، فإذا كان mST = 144°، فأوجد m∠R؟

المثال 2 جبر: أوجد كلاً من القياسين الآتيين:

5) m∠H

6) m∠B

7) برهان: اكتب برهانًا ذا عمودين. المعطيات: RT تنصف SU. المطلوب: ΔUVT ≅ ΔRVS

المثالان 4, 5 جبر: أوجد قيمة كل مما يأتي:

8) m∠R

9) x

10) m∠C, m∠D

تدرب وحل المسائل

المثال 1 أوجد كل قياس مما يأتي:

11) mDH

12) m∠K

13) m∠P

وزارة التعليم الدرس 4-8 الزوايا المحيطية 205 MI205 of Education 2025 - 1447

--- SECTION: تأكد --- تأكد --- SECTION: المثال 1 --- المثال 1 أوجد كل قياس مما يأتي: --- SECTION: 1 --- 1) m∠B --- SECTION: 2 --- 2) mRT --- SECTION: 3 --- 3) mWX --- SECTION: 4 --- 4) علوم: يبين الشكل المجاور انكسار أشعة الضوء في قطرة مطر لإنتاج ألوان الطيف، فإذا كان mST = 144°، فأوجد m∠R؟ --- SECTION: المثال 2 --- المثال 2 جبر: أوجد كلاً من القياسين الآتيين: --- SECTION: 5 --- 5) m∠H --- SECTION: 6 --- 6) m∠B --- SECTION: 7 --- 7) برهان: اكتب برهانًا ذا عمودين. المعطيات: RT تنصف SU. المطلوب: ΔUVT ≅ ΔRVS --- SECTION: المثالان 4, 5 --- المثالان 4, 5 جبر: أوجد قيمة كل مما يأتي: --- SECTION: 8 --- 8) m∠R --- SECTION: 9 --- 9) x --- SECTION: 10 --- 10) m∠C, m∠D --- SECTION: تدرب وحل المسائل --- تدرب وحل المسائل --- SECTION: المثال 1 --- المثال 1 أوجد كل قياس مما يأتي: --- SECTION: 11 --- 11) mDH --- SECTION: 12 --- 12) m∠K --- SECTION: 13 --- 13) m∠P وزارة التعليم الدرس 4-8 الزوايا المحيطية 205 MI205 of Education 2025 - 1447 --- VISUAL CONTEXT --- **DIAGRAM**: Untitled Description: A circle with points A, B, C on its circumference. An inscribed angle ∠B is shown, subtending arc AC. The measure of arc AC is given as 60°. Context: Illustrates the relationship between an inscribed angle and its intercepted arc. **DIAGRAM**: Untitled Description: A circle with points R, S, T on its circumference. An inscribed angle ∠S is shown, subtending arc RT. The measure of angle ∠S is given as 63°. Context: Illustrates the relationship between an inscribed angle and its intercepted arc. **DIAGRAM**: Untitled Description: A circle with points W, X, Y on its circumference. A chord WY passes through the center of the circle (indicated by a central dot on WY), making it a diameter. An inscribed angle subtends arc WX. The measure of an angle related to arc WX is 57°. This angle appears to be an inscribed angle subtending arc WX. Context: Illustrates properties of inscribed angles and angles subtended by a diameter. **IMAGE**: Untitled Description: A diagram illustrating the phenomenon of light refraction and dispersion within a spherical water droplet (raindrop), leading to the formation of a rainbow. A white light ray, labeled 'S', enters the droplet, undergoes refraction, then internal reflection, and finally refracts again upon exiting, labeled 'T', splitting into a spectrum of colors. Point 'R' is marked on the surface of the droplet where the light enters. Context: Visualizes the physics of light and optics, specifically refraction and dispersion in a raindrop to explain rainbows, relevant to the geometry of angles and arcs in a circular context. **DIAGRAM**: Untitled Description: A circle with an inscribed quadrilateral GHKJ. Angle ∠H is labeled x°. Arc GK is labeled (2x - 54)°. The diagonals GK and HJ are drawn, intersecting inside the circle. Context: Illustrates properties of inscribed angles and arcs in a cyclic quadrilateral. **DIAGRAM**: Untitled Description: A circle with an inscribed quadrilateral ABCD. Angle ∠B is labeled (x + 24)°. Arc CD is labeled 3x°. The diagonals AC and BD are drawn, intersecting inside the circle. Context: Illustrates properties of inscribed angles and arcs in a cyclic quadrilateral. **DIAGRAM**: Untitled Description: A circle with two chords, RT and SU, intersecting at point V inside the circle. The problem statement indicates that RT bisects SU, meaning SV = VU. The diagram shows points R, S, T, U on the circumference. Context: Used for a geometric proof involving congruent triangles formed by intersecting chords in a circle. **DIAGRAM**: Untitled Description: A circle with an inscribed quadrilateral PQRS. Angle ∠P is labeled (3x + 1)°. Arc QR is labeled (7x - 1)°. The diagonals PR and QS are drawn, intersecting inside the circle. Context: Illustrates properties of inscribed angles and arcs in a cyclic quadrilateral, requiring algebraic solution. **DIAGRAM**: Untitled Description: A circle with an inscribed quadrilateral LMNP. Chord LN passes through the center of the circle (indicated by a central dot on LN), making it a diameter. Arc NP and arc LM are marked with two tick marks each, indicating they are congruent (NP = LM). Arc MN is labeled (2x - 5)°. Context: Illustrates properties of inscribed quadrilaterals, congruent arcs, and arcs formed by a diameter, requiring algebraic solution. **DIAGRAM**: Untitled Description: A circle with an inscribed quadrilateral ABCD. The center of the circle is marked with a dot. Arc AB is labeled 58°. Angle ∠B is labeled (3y + 4)°. Angle ∠C is labeled 2x°. Angle ∠D is labeled (2y + 16)°. Context: Illustrates properties of inscribed quadrilaterals and their angles and intercepted arcs, requiring algebraic solution for two variables. **DIAGRAM**: Untitled Description: A circle with points D, F, H on its circumference. An inscribed angle ∠F is shown, subtending arc DH. The measure of angle ∠F is given as 81°. Context: Illustrates the relationship between an inscribed angle and its intercepted arc. **DIAGRAM**: Untitled Description: A circle with points J, K, L on its circumference. An inscribed angle ∠K is shown, subtending arc JL. The measure of arc JL is given as 92°. Context: Illustrates the relationship between an inscribed angle and its intercepted arc. **DIAGRAM**: Untitled Description: A circle with an inscribed quadrilateral NPQ. Arc NP is labeled 120°. Arc PQ is labeled 100°. Angle ∠P is an inscribed angle. Context: Illustrates properties of inscribed angles and arcs in a cyclic quadrilateral.