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the triangles below are congruent and their corresponding parts are mar…

(a) $\angle A \cong \angle Y$,$\angle B \cong \angle Z$,$\angle C \cong \angle X$ (b) $\overline{AB} \cong \overline{YZ}$,$\overline{AC} \cong \overline{XY}$,$\overline{BC} \cong …

分类: geometry 更新时间: 2026-02-09

题目

the triangles below are congruent and their corresponding parts are marked.

name all the corresponding congruent angles and sides.
then, complete the triangle congruence statement.
(a) $angle a \\cong \\angle \\square$
$angle b \\cong \\angle \\square$
$angle c \\cong \\angle \\square$
(b) $overline{ab} \\cong \\overline{\\square}$
$overline{ac} \\cong \\overline{\\square}$
$overline{bc} \\cong \\overline{\\square}$
(c) $\triangle abc \\cong \\triangle \\square$

解题步骤

  1. Understand the question

    the triangles below are congruent and their corresponding parts are marked.

    name all the corresponding congruent angles and sides.
    then, complete the triangle congruence statement.
    (a) $angle a \\cong \\angle \\square$
    $angle b \\cong \\angle \\square$
    $angle c \\cong \\angle \\square$
    (b) $overline{ab} \\cong \\overline{\\square}$
    $overline{ac} \\cong \\overline{\\square}$
    $overline{bc} \\cong \\overline{\\square}$
    (c) $\triangle abc \\cong \\triangle \\square$

  2. Explanation

    Step1: 匹配对应角

    根据标记的全等对应关系:
    $\angle A \cong \angle Y$,$\angle B \cong \angle Z$,$\angle C \cong \angle X$

    Step2: 匹配对应边

    根据标记的全等对应关系:
    $\overline{AB} \cong \overline{YZ}$,$\overline{AC} \cong \overline{XY}$,$\overline{BC} \cong \overline{ZX}$

    Step3: 写出全等三角形

    根据对应顶点的对应关系,得到:
    $\triangle ABC \cong \triangle YZX$

  3. Final answer

    (a) $\angle A \cong \angle Y$,$\angle B \cong \angle Z$,$\angle C \cong \angle X$
    (b) $\overline{AB} \cong \overline{YZ}$,$\overline{AC} \cong \overline{XY}$,$\overline{BC} \cong \overline{ZX}$
    (c) $\triangle ABC \cong \triangle YZX$

答案

Explanation

Step1: 匹配对应角

根据标记的全等对应关系:
$\angle A \cong \angle Y$,$\angle B \cong \angle Z$,$\angle C \cong \angle X$

Step2: 匹配对应边

根据标记的全等对应关系:
$\overline{AB} \cong \overline{YZ}$,$\overline{AC} \cong \overline{XY}$,$\overline{BC} \cong \overline{ZX}$

Step3: 写出全等三角形

根据对应顶点的对应关系,得到:
$\triangle ABC \cong \triangle YZX$

Answer

(a) $\angle A \cong \angle Y$,$\angle B \cong \angle Z$,$\angle C \cong \angle X$
(b) $\overline{AB} \cong \overline{YZ}$,$\overline{AC} \cong \overline{XY}$,$\overline{BC} \cong \overline{ZX}$
(c) $\triangle ABC \cong \triangle YZX$

Question Image

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Question Analysis

Subject mathematics
Sub Subject geometry
Education Level high school
Difficulty unspecified
Question Type with image
Multi Question No
Question Count 1
Analysis Status completed
Analyzed At 2026-02-09T20:08:57

OCR Text

Show OCR extraction
the triangles below are congruent and their corresponding parts are marked.

name all the corresponding congruent angles and sides.
then, complete the triangle congruence statement.
(a) $angle a \\cong \\angle \\square$
$angle b \\cong \\angle \\square$
$angle c \\cong \\angle \\square$
(b) $overline{ab} \\cong \\overline{\\square}$
$overline{ac} \\cong \\overline{\\square}$
$overline{bc} \\cong \\overline{\\square}$
(c) $\triangle abc \\cong \\triangle \\square$

相关知识点

mathematicsgeometrywith imagehigh schoolturns-1

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