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

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

Category: geometry Updated: 2026-02-09

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) $\triangle cba \\cong \\triangle \\square$

Solution Steps

  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) $\triangle cba \\cong \\triangle \\square$

  2. Explanation

    Step1: 匹配对应角

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

    Step2: 匹配对应边

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

    Step3: 写出全等三角形

    结合对应顶点的匹配,$\triangle CBA$的对应全等三角形为$\triangle YXZ$,即:
    $\triangle CBA \cong \triangle YXZ$

  3. Final answer

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

Answer

Explanation

Step1: 匹配对应角

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

Step2: 匹配对应边

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

Step3: 写出全等三角形

结合对应顶点的匹配,$\triangle CBA$的对应全等三角形为$\triangle YXZ$,即:
$\triangle CBA \cong \triangle YXZ$

Answer

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

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 2026-02-09T20:08:01

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) $\triangle cba \\cong \\triangle \\square$

Related Topics

mathematicsgeometrywith imagehigh schoolturns-1

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