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

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

Catégorie: geometry Mis à jour: 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) $\triangle bca \\cong \\triangle \\square$

Étapes de solution

  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) $\triangle bca \\cong \\triangle \\square$

  2. Explanation

    Step1: 匹配对应角

    根据标记的全等对应关系,$\angle A$(双弧线)对应$\angle X$(双弧线),$\angle B$对应$\angle Y$,$\angle C$(单弧线)对应$\angle Z$(单弧线)。
    $\angle A \cong \angle X$,$\angle B \cong \angle Y$,$\angle C \cong \angle Z$

    Step2: 匹配对应边

    根据标记的全等对应关系,$\overline{AB}$(双杠)对应$\overline{ZY}$(双杠),$\overline{AC}$(单杠)对应$\overline{XY}$(单杠),$\overline{BC}$(三杠)对应$\overline{ZX}$(三杠)。
    $\overline{AB} \cong \overline{ZY}$,$\overline{AC} \cong \overline{XY}$,$\overline{BC} \cong \overline{ZX}$

    Step3: 写出全等三角形

    结合对应角和边的匹配,$\triangle BCA$的对应全等三角形为$\triangle YZX$。
    $\triangle BCA \cong \triangle YZX$

  3. Final answer

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

Réponse

Explanation

Step1: 匹配对应角

根据标记的全等对应关系,$\angle A$(双弧线)对应$\angle X$(双弧线),$\angle B$对应$\angle Y$,$\angle C$(单弧线)对应$\angle Z$(单弧线)。
$\angle A \cong \angle X$,$\angle B \cong \angle Y$,$\angle C \cong \angle Z$

Step2: 匹配对应边

根据标记的全等对应关系,$\overline{AB}$(双杠)对应$\overline{ZY}$(双杠),$\overline{AC}$(单杠)对应$\overline{XY}$(单杠),$\overline{BC}$(三杠)对应$\overline{ZX}$(三杠)。
$\overline{AB} \cong \overline{ZY}$,$\overline{AC} \cong \overline{XY}$,$\overline{BC} \cong \overline{ZX}$

Step3: 写出全等三角形

结合对应角和边的匹配,$\triangle BCA$的对应全等三角形为$\triangle YZX$。
$\triangle BCA \cong \triangle YZX$

Answer

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

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 2026-02-09T20:10:32

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) $\triangle bca \\cong \\triangle \\square$

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