请严格按照这几张图片的内容，帮我生成视频---Here is the extracted content from the image: **Title:** 基本概念 (Basic Concepts) **Definition:** * 定义 (Definition) 飞镖模型是指四边形其中一个内角大于180°的凹四边形，形似飞镖。 (A dart model refers to a concave quadrilateral where one of its interior angles is greater than 180°, resembling a dart.) **Figure Characteristics:** * 图形特征 (Figure Characteristics) * 有一个内角为优角 ( >180°) (One interior angle is a reflex angle (>180°)) * 两组邻边分别相等 (Two pairs of adjacent sides are equal) * 对角线相交于形外 (Diagonals intersect outside the figure) **Constituent Elements:** * 构成要素 (Constituent Elements) * 4个顶点 (A、B、C、D) (4 vertices (A, B, C, D)) * 4条边 (AB、BC、CD、DA) (4 sides (AB, BC, CD, DA)) * 3个内角 (其中1个优角) (3 interior angles (including 1 reflex angle)) **Chart/Diagram Description:** **Chart Title:** 图: 飞镖模型示意图 (标注顶点与优角) (Figure: Dart Model Schematic Diagram (Vertices and Reflex Angles Marked)) **Content within the Chart/Diagram Area:** **Section Title:** 模型二：飞镖模型 (Model Two: Dart Model) **Top Left Figure (Figure 1):** * **Type:** Geometric figure (Concave Quadrilateral) * **Main Elements:** * A concave quadrilateral with vertices A, B, C, D. * Vertex D is the concave vertex, representing the reflex angle. * Lines: Segments AB, BC, CD, DA forming the quadrilateral. * **Associated Text:** 条件: 四边形ABCD 如左图所示。 (Condition: Quadrilateral ABCD is as shown in the left figure.) **Top Right Figure (Figure 2):** * **Type:** Geometric figure (Concave Quadrilateral with auxiliary line) * **Main Elements:** * A concave quadrilateral with vertices A, B, C, D, similar to Figure 1. * An auxiliary line segment AD is extended to point E. * Angles are labeled '1' and '2' inside the triangles formed by the extension. Angle '1' is ∠ADB, Angle '2' is ∠ADC. (Note: The diagram shows angles marked as ∠1 and ∠2, likely referring to parts of ∠BDC, where ∠1 is ∠ADE and ∠2 is ∠CDE). * **Associated Text:** 结论: ∠D=∠A+∠B+∠C。(凹四边形外角等于三个内角和) (Conclusion: ∠D=∠A+∠B+∠C. (The exterior angle of a concave quadrilateral equals the sum of the three interior angles)) 证明: 如上右图，连接AD并延长到E，则：∠BDC=∠BDE+∠CDE=(∠B+∠1)+(∠C+∠2)=∠B+∠BAC+∠BCA。同理证明。 (Proof: As shown in the upper right figure, connect AD and extend it to E, then: ∠BDC=∠BDE+∠CDE=(∠B+∠1)+(∠C+∠2)=∠B+∠BAC+∠BCA. Proved similarly.) **Bottom Left Figure (Figure 3):** * **Type:** Complex geometric figure (intersecting lines forming two "dart" shapes) * **Main Elements:** * A multi-vertex figure (star-like or two overlapping concave quadrilaterals). * Vertices are A, B, C, D, E, F. * Multiple line segments intersect. * An angle is explicitly marked as 130° at the central intersection point, labeled E. * **Associated Text:** 应用: 如下左图，则∠A+∠B+∠C+∠D+∠E+∠F=260°（下图中两个飞镖）。 (Application: As shown in the lower left figure, then ∠A+∠B+∠C+∠D+∠E+∠F=260° (two darts in the figure below).) **Bottom Right Figure (Figure 4):** * **Type:** Complex geometric figure (intersecting lines) * **Main Elements:** * A multi-vertex figure. * Vertices are A, B, C, D, E. * An angle is marked as 70° near vertex E. The line segments form a shape. Here is the extracted content from the image: **Overall Title:** 验证过程 (Verification Process) --- **Section 1: General Proof/Derivation (Left Panel)** **Topic:** 利用三角形外角定理推导飞镖模型内角关系: (Using the triangle exterior angle theorem to derive the relationship between interior angles of the dart model:) **Proof Steps:** 1. 连接BD并延长至点E (Connect BD and extend to point E) 2. ∠ADC = ∠CDE + ∠ADE 3. 由三角形外角性质得: ∠CDE = ∠C + ∠CBD (From the property of triangle exterior angles: ∠CDE = ∠C + ∠CBD) 4. 最终推导得: ∠ADC = ∠A + ∠B + ∠C (Finally derived: ∠ADC = ∠A + ∠B + ∠C) **Theorem Conclusion:** 定理结论 (Theorem Conclusion) 飞镖模型中, 优角等于其余三个内角之和 (In the dart model, the reflex angle is equal to the sum of the other three interior angles.) --- **Section 2: Specific Problem (Right Panel)** **Problem Statement:** 如图，凹四边形ABOC。 (As shown in the figure, concave quadrilateral ABOC.) 求证: ∠A + ∠B + ∠C = ∠BOC. (Prove: ∠A + ∠B + ∠C = ∠BOC.) **Model Label/Annotation:** 燕尾模型 (Swallowtail Model) **Chart/Diagram Description:** * **Type:** Geometric Figure (Concave Quadrilateral). * **Main Elements:** * **Points:** Four labeled vertices A, B, O, C. Point O is located "inside" the triangle formed by A, B, C if lines AB, AC, BC were drawn, indicating it's the concave vertex. * **Lines:** Line segments connect the vertices to form the concave quadrilateral ABOC. These segments are AB, BO, OC, and CA. * **Angles:** The problem refers to angles ∠A (likely ∠BAC), ∠B (likely ∠ABO), ∠C (likely ∠ACO), and ∠BOC (the interior angle at the concave vertex O). * **Legend/Footnote:** 图: 带辅助线的飞镖模型证明示意图 (Figure: Schematic diagram of the dart model proof with auxiliary lines) **Extraction Content:** **I. General Information / Application Context** * **Header:** 应用场景 (Application Scenarios) * **Applicable Problem Types (适用题型):** * 求凹四边形内角和 (Calculate the sum of interior angles of a concave quadrilateral) * 证明角度等量关系 (Prove angle equality relationships) * 辅助线添加技巧训练 (Auxiliary line addition technique training) * **Problem Solving Techniques (解题技巧):** * 遇凹四边形优先考虑飞镖模型 (Prioritize considering the dart model when encountering concave quadrilaterals) * 构造辅助线转化为三角形问题 (Construct auxiliary lines to transform into triangle problems) * 利用内角关系建立方程 (Use interior angle relationships to set up equations) * **Common Mistakes (常见错误):** * 忽略优角特殊性 (Neglecting the particularity of reflex angles) * 辅助线添加不当导致思路混乱 (Improper auxiliary line addition leading to confusion in thought) **II. Question and Related Content** * **Question Number:** 35. * **Question Stem:** * (1) 探究：如图1，求证：∠BOC = ∠A + ∠B + ∠C. (Explore: As shown in Figure 1, prove: ∠BOC = ∠A + ∠B + ∠C.) * (2) 应用：如图2，∠ABC = 100°，∠DEF = 130°，求∠A + ∠C + ∠D + ∠F 的度数. (Application: As shown in Figure 2, ∠ABC = 100°, ∠DEF = 130°, find the degree measure of ∠A + ∠C + ∠D + ∠F.) * **Annotation (in red box):** 初中数学经典几何模型：飞镖模型 (Middle School Mathematics Classic Geometric Model: Dart Model) * **Image Caption:** 图：飞镖模型在不同题型中的应用示例 (Figure: Application examples of the Dart Model in different problem types) * **Interactive Toolbar (below the images):** * Buttons/Icons: 关闭 (Close), 选择 (Select), 画笔 (Pen), 擦除 (Erase), 截图 (Screenshot), 互动 (Interact). * Additional text/icons: "http://www", "0101", a circular timer icon (00:00). **III. Chart/Diagram Description** * **Overall Context:** The images are presented within a digital interface, possibly a screenshot from a presentation or an online learning platform, indicated by the interactive toolbar at the bottom and the window title-like element at the top right (containing "00:00"). * **Figure 1 (图1):** * **Type:** Geometric figure, specifically a concave quadrilateral (commonly known as a "dart" or "arrowhead" shape in geometry). * **Main Elements:** * **Points:** Labeled A, B, C, O. Point O is the concave vertex of the quadrilateral. * **Lines:** Straight line segments AB, BC, CO, and OA form the boundary of the concave quadrilateral. The segment AC is implied to form a triangle ABC from which the dart shape is derived, or defines the "outer" boundary of the dart. * **Labels:** "图1" is labeled below the figure. * **Figure 2 (图2):** * **Type:** Geometric figure, composed of two separate concave quadrilateral shapes (two "dart" shapes). * **Main Elements:** * **Points:** Labeled A, B, C, D, E, F. Each of the two dart shapes has three labeled outer vertices (A, B, C for the left one; D, E, F for the right one) and an implied unlabeled concave vertex. * **Lines:** Straight line segments form the boundaries of the two shapes. The left shape consists of vertices A, B, C, and an internal concave vertex (unlabeled). The right shape consists of vertices D, E, F, and an internal concave vertex (unlabeled). * **Angles:** * ∠ABC is explicitly labeled with a value of 100°. * ∠DEF is explicitly labeled with a value of 130°. * These angles (∠ABC, ∠DEF) appear to be interior angles at vertices B and E respectively, which are convex vertices of their respective "dart" shapes. * **Labels:** "图2" is labeled below the figure. **Main Title:** 例题解析 (Example Problem Analysis) --- **Question 1:** **Question Stem:** 题目 (Problem) 在飞镖模型ABCD中，∠A=30°, ∠B=40°, ∠C=25°, 求∠ADC的度数。 (In dart model ABCD, ∠A=30°, ∠B=40°, ∠C=25°, find the measure of ∠ADC.) **Solution Steps:** 解题步骤 (Solution Steps) 1. 根据飞镖模型定理：∠ADC = ∠A + ∠B + ∠C (According to the dart model theorem: ∠ADC = ∠A + ∠B + ∠C) 2. 代入数据：∠ADC = 30° + 40° + 25° (Substitute data: ∠ADC = 30° + 40° + 25°) 3. 计算：30° + 40° = 70°, 70° + 25° = 95° (Calculate: 30° + 40° = 70°, 70° + 25° = 95°) **Answer:** 答案 (Answer) ∠ADC = 95° --- **Question 2 (from Diagram and Handwritten Notes):** **Question Stem:** 如图所示，∠A=50°, ∠B=20°, ∠D=30°, 则∠BCD的度数为 ( ) (As shown in the figure, ∠A=50°, ∠B=20°, ∠D=30°, then the measure of ∠BCD is ( )) **Chart/Diagram Description:** * **Type:** Geometric figure (a concave quadrilateral, often called a "dart" or "arrowhead" shape). * **Main Elements:** * **Vertices:** Labeled A (top), B (left), C (inside, concave vertex), D (right). * **Lines:** Solid lines form the perimeter of the quadrilateral ABCD. * Segment AB, BC, CD, DA. * **Auxiliary Line:** A dashed line segment starting from vertex A, passing through the concave vertex C, and extending downwards. * **Angles:** * At vertex A, the angle is split by the dashed line into two parts, labeled '3' (left part) and '4' (right part). * At vertex C (the concave vertex), the angle ∠BCD is split by the dashed line into two parts, labeled '1' (left part, adjacent to BC) and '2' (right part, adjacent to CD). * Angles at B and D are not explicitly split by labels within the diagram, but their values are given in the question stem. * **Handwritten Notes (likely derivation steps or thought process):** * ∠1 = ∠B + ∠4 * ∠2 = ∠3 + ∠D * ∠BCD = ∠1 + ∠2 **Other Relevant Text:** 图：例题飞镖模型图 (标注已知角度和所求角度) (Figure: Example dart model diagram (labeled known angles and required angle)) **Overall Summary** The image presents a "Learning Summary" for geometry, specifically focusing on angle models in triangles and related concepts. It includes sections for "Key Review," "Learning Suggestions," and "Further Thoughts," alongside a detailed table summarizing various angle models, their diagrams, and corresponding conclusions/formulas. --- **Textual Information** **Title:** 学习总结 (Learning Summary) **Section: 重点回顾 (Key Review)** * 飞镖模型的定义与特征 (Definition and characteristics of the dart model) * 内角关系定理及证明 (Theorem and proof of internal angle relationships) * 辅助线添加技巧 (Skills for adding auxiliary lines) **Section: 学习建议 (Learning Suggestions)** * 多做变式练习巩固定理应用 (Do more varied exercises to consolidate theorem application) * 结合三角形知识综合运用 (Comprehensive application of triangle knowledge) * 总结辅助线添加规律 (Summarize rules for adding auxiliary lines) **Section: 拓展思考 (Further Thoughts)** * 飞镖模型与凸四边形的区别 (Distinction between the dart model and convex quadrilaterals) * 如何用坐标法证明飞镖模型定理 (How to prove the dart model theorem using coordinate method) --- **Table Content** **Table Title:** 三角形中角度模型汇总 (Summary of Angle Models in Triangles) | 名称 (Name) | 图形 (Figure) | | |---|---|---| | 八字模型 (Figure-eight model) | Diagram of two triangles forming an X shape. Labels: A, B, C, D, O. Lines: AC and BD intersect at O. | Angle A + Angle B = Angle C + Angle D | | 飞镖模型 (Dart model) | Diagram of a concave quadrilateral (dart shape). Labels: A, B, C, D. Point D is the concave vertex. | Angle D = Angle A + Angle B + Angle C | | 两内角角平分线模型 (Two internal angle bisector model) | Diagram of a triangle ABC. Angle bisectors from B and C intersect at point I. Angles are labeled 1, 2, 3, 4. | Angle I = 90° + (1/2) Angle A | | 两外角角平分线模型 (Two external angle bisector model) | Diagram of a triangle ABC. Sides AB and AC are extended to E and F. External angle bisectors from B (for ∠CBE) and C (for ∠BCF) intersect at point O. Angles are labeled 5, 6. | Angle O = 90° - (1/2) Angle A | | 内外角平分线模型 (Internal and external angle bisector model) | Diagram of a triangle ABC. An internal angle bisector from B for ∠ABC. An external angle bisector from C for ∠ACE (where E is on the extension of BC). The two bisectors intersect at P. | Angle P = (1/2) Angle A | --- **Chart/Diagram Description** The image includes a table containing five geometric figures, each illustrating a specific "angle model." * **Figure 1: 八字模型 (Figure-eight model)** * **Type:** Geometric figure, two intersecting triangles (e.g., ΔAOB and ΔCOD). * **Main Elements:** * **Points:** Labeled A, B, C, D, and O (intersection point of AC and BD). * **Lines:** Straight lines AC and BD intersect at O. Lines AD, AB, BC, CD form two triangles. * **Shapes:** Appears to be a quadrilateral ABCD with its diagonals intersecting, or two triangles ΔAOD and ΔBOC (or ΔAOB and ΔDOC) connected at a vertex O. The figure looks like an 'X'. * **Angles:** Implied angles at vertices A, B, C, D. * **Figure 2: 飞镖模型 (Dart model)** * **Type:** Geometric figure, a concave quadrilateral. * **Main Elements:** * **Points:** Labeled A, B, C, D. Point D is the inward-pointing (concave) vertex. * **Lines:** Straight lines AB, BC, CD, DA forming a four-sided figure where one interior angle (at D) is greater than 180 degrees. * **Shapes:** A concave quadrilateral, resembling a "dart" or "arrowhead" shape. * **Figure 3: 两内角角平分线模型 (Two internal angle bisector model)** * **Type:** Geometric figure, a triangle with two internal angle bisectors. * **Main Elements:** * **Points:** Labeled A, B, C (vertices of a triangle), and I (intersection point of the angle bisectors). * **Lines:** Straight lines forming triangle ABC. Line BI bisects ∠ABC. Line CI bisects ∠ACB. * **Angles:** Angles labeled 1, 2, 3, 4. ∠1 = ∠2 (halves of ∠ABC). ∠3 = ∠4 (halves of ∠ACB). ∠I is the angle at the intersection point I. * **Figure 4: 两外角角平分线模型 (Two external angle bisector model)** * **Type:** Geometric figure, a triangle with two external angle bisectors. * **Main Elements:** * **Points:** Labeled A, B, C (vertices of a triangle), and E, F (points on extensions of sides AB and AC, respectively), and O (intersection point of the external angle bisectors). * **Lines:** Straight lines forming triangle ABC. Line BE extends AB. Line CF extends AC. Line BO bisects the exterior angle at B (∠CBE). Line CO bisects the exterior angle at C (∠BCF). * **Angles:** Angles labeled 5, 6. ∠5 is half of the exterior angle at B. ∠6 is half of the exterior angle at C. ∠O is the angle at the intersection point O. * **Figure 5: 内外角平分线模型 (Internal and external angle bisector model)** * **Type:** Geometric figure, a triangle with one internal and one external angle bisector. * **Main Elements:** * **Points:** Labeled A, B, C (vertices of a triangle), P (intersection point), and E (point on extension of BC). * **Lines:** Straight lines forming triangle ABC. Line BP bisects ∠ABC. Line CP bisects the exterior angle at C (∠ACE), where E is on the extension of BC. * **Angles:** ∠P is the angle at the intersection point P. --- **Caption:** 图：飞镖模型知识结构图 (Figure: Dart Model Knowledge Structure Diagram)