Geometry II: Further Theorems Practice Questions
1.
What more do you need to know in the diagram on the right in order to prove
congruency by:
(i)
ASA
?
|
BAC
| = |
ACD
|
SAS
?
|
AD
| = |
BC
|
(ii)
2.
From the information in the diagram, can you prove Δ
FDG
≡ Δ
FDE
?
Explain your answer.
FDG
FDE
|
GDF
|
= |
EDF
|
Given in diagram
|
DF
| = |
DF
|
Common to both triangles
|
DFG
|
= |
DFE
|
Given in diagram
FDG
FDB
by
ASA
3.
State whether Δ
ABC
and Δ
AED
are congruent.
Justify your answer.
ABC
AED
|
AB
|
=
|
AE
|
Both 7 in diagram
|
BAC
|
=
|
DAE
|
Given in diagram
|
AC
|
=
|
AD
|
Given in diagram
ABC
AED
by
SAS
4.
Is there enough information to prove the two triangles are congruent in each of the
following?
If so, write down the method that would be used.
If not, explain why not.
(i)
No
Given; side, side, angle
The given angle is not between two sides, so no, as there is no
SSA
axiom.
4.
Is there enough information to prove the two triangles are congruent in each of the
following?
If so, write down the method that would be used.
If not, explain why not.
(ii)
Yes ;
SAS
4.
Is there enough information to prove the two triangles are congruent in each of the
following?
If so, write down the method that would be used.
If not, explain why not.
(iii)
Yes ;
RHS
4.
Is there enough information to prove the two triangles are congruent in each of the
following?
If so, write down the method that would be used.
If not, explain why not.
(iv)
Yes ;
ASA
4.
Is there enough information to prove the two triangles are congruent in each of the
following?
If so, write down the method that would be used.
If not, explain why not.
(v)
Yes ;
SSS
4.
Is there enough information to prove the two triangles are congruent in each of the
following?
If so, write down the method that would be used.
If not, explain why not.
(vi)
No
Given ; Angle, Angle, Angle
No
AAA
axiom
4.
Is there enough information to prove the two triangles are congruent in each of the
following?
If so, write down the method that would be used.
If not, explain why not.
(vii)
Yes ;
RHS
4.
Is there enough information to prove the two triangles are congruent in each of the
following?
If so, write down the method that would be used.
If not, explain why not.
(viii)
Yes ;
SAS
5.
An architect is designing a window in a house as shown in the picture.
He wants to make
Δ
XYT
congruent to
Δ
ZYT
.
He designs the window so that
|
XY|
= |
YZ|
and
|
XYT|
= |
ZYT|
.
Prove that
Δ
XYT
is congruent to
Δ
ZYT
.
XYT
ZYT
|
XY
| = |
YZ
| Given
|
XYT
| = |
ZYT
| Given
|
YT
| = |
YT
| Common to both triangles
XYT
ZYT
by
SAS
Explore practice questions on congruency in triangles through the ASA, SAS, and other methods. From proving congruency to justifying answers, enhance your understanding of geometry concepts.
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Presentation Transcript
CHAPTER 11 Geometry II: Further Theorems Solutions: Practice Questions 11.2
11 Practice Questions 11.2 1. What more do you need to know in the diagram on the right in order to prove congruency by: ASA? (i) | BAC| = | ACD| SAS? (ii) |AD| = |BC|
11 Practice Questions 11.2 2. From the information in the diagram, can you prove FDG FDE? Explain your answer. FDG FDE | GDF|= | EDF| Given in diagram |DF| = |DF| Common to both triangles | DFG|= | DFE| Given in diagram FDG FDB by ASA
11 Practice Questions 11.2 3. State whether ABC and AED are congruent. Justify your answer. ABC AED |AB| = |AE| Both 7 in diagram | BAC| = | DAE|Given in diagram |AC| = |AD| Given in diagram ABC AED by SAS
11 Practice Questions 11.2 4. Is there enough information to prove the two triangles are congruent in each of the following? If so, write down the method that would be used. If not, explain why not. (i) No Given; side, side, angle The given angle is not between two sides, so no, as there is no SSA axiom.
11 Practice Questions 11.2 4. Is there enough information to prove the two triangles are congruent in each of the following? If so, write down the method that would be used. If not, explain why not. (ii) Yes ; SAS
11 Practice Questions 11.2 4. Is there enough information to prove the two triangles are congruent in each of the following? If so, write down the method that would be used. If not, explain why not. (iii) Yes ; RHS
11 Practice Questions 11.2 4. Is there enough information to prove the two triangles are congruent in each of the following? If so, write down the method that would be used. If not, explain why not. (iv) Yes ; ASA
11 Practice Questions 11.2 4. Is there enough information to prove the two triangles are congruent in each of the following? If so, write down the method that would be used. If not, explain why not. (v) Yes ; SSS
11 Practice Questions 11.2 4. Is there enough information to prove the two triangles are congruent in each of the following? If so, write down the method that would be used. If not, explain why not. (vi) No Given ; Angle, Angle, Angle No AAA axiom
11 Practice Questions 11.2 4. Is there enough information to prove the two triangles are congruent in each of the following? If so, write down the method that would be used. If not, explain why not. (vii) Yes ; RHS
11 Practice Questions 11.2 4. Is there enough information to prove the two triangles are congruent in each of the following? If so, write down the method that would be used. If not, explain why not. (viii) Yes ; SAS
11 Practice Questions 11.2 5. An architect is designing a window in a house as shown in the picture. He wants to make XYTcongruent to ZYT. He designs the window so that |XY| = |YZ|and | XYT| = | ZYT|. Prove that XYTis congruent to ZYT. XYT ZYT |XY| = |YZ| Given | XYT| = | ZYT| Given |YT| = |YT| Common to both triangles XYT ZYT by SAS
