Question

In Exercises 13 to $18,$ use only the given information to state the reason why $\triangle A B C \cong \triangle D B C .$ Redraw the figure and use marks like those used in Exercises 9 to 12 . $$\angle 1 \text { and } \angle 2 \text { are right } \angle \mathrm{s}, \overline{A B} \equiv \overline{B D}, \text { and } \angle A \equiv \angle D$$ (GRAPH CANT COPY)

Name: Problem 18, Chapter 3: Elementary Geometry for College Students
Uploaded: 2021-11-19T23:33:58-08:00
Duration: 41 s
Channel: James Kiss
Description: In Exercises 13 to 18, use only the given information to state the reason why A B C ≅D B C . Redraw the figure and use marks like those used in Exercises 9 to 12 . ∠1 and ∠2 are right ∠s, A B ≡B D, and ∠A ≡∠D (GRAPH CANT COPY)

   In Exercises 13 to $18,$ use only the given information to state the reason why $\triangle A B C \cong \triangle D B C .$ Redraw the figure and use marks like those used in Exercises 9 to 12 .
$$\angle 1 \text { and } \angle 2 \text { are right } \angle \mathrm{s}, \overline{A B} \equiv \overline{B D}, \text { and } \angle A \equiv \angle D$$
(GRAPH CANT COPY)

Elementary Geometry for College Students

Daniel C. Alexander,… 6th Edition

Chapter 3, Problem 18

Instant Answer

Solved by Expert James Kiss

11/19/2021

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By the definition of right angles, we know that $\angle 1 \cong \angle 2$. Show more…

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In Exercises 13 to $18,$ use only the given information to state the reason why $\triangle A B C \cong \triangle D B C .$ Redraw the figure and use marks like those used in Exercises 9 to 12 . $$\angle 1 \text { and } \angle 2 \text { are right } \angle \mathrm{s}, \overline{A B} \equiv \overline{B D}, \text { and } \angle A \equiv \angle D$$ (GRAPH CANT COPY)

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Key Concepts

Triangle Congruence Criteria

This concept involves the sets of conditions (such as ASA, AAS, SAS, SSS, and for right triangles, HL) that, when satisfied, guarantee that two triangles are congruent. By checking for congruent pairs of angles and sides, one can conclude that all corresponding parts of the triangles are equal.

Right Triangle Hypotenuse?Leg (HL) Theorem

For right triangles, the HL theorem states that if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, then the triangles are congruent. This is a specialized congruence criterion that applies when the triangles each have a right angle.

Reflexive Property

In geometry, the reflexive property asserts that any geometric element (such as a side in a triangle) is congruent to itself. This principle is often used in congruence proofs when the triangles share a common side or angle.

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